Systems and methods for transverse energy localization in energy relays using ordered structures

ABSTRACT

Disclosed are systems and methods for manufacturing energy relays for energy directing systems inducing Ordered Energy Localization effects. Ordered Energy Localization relay material distribution criteria are disclosed. Transverse planar as well as multi-dimensional ordered material configurations are discussed. Methods and systems are disclosed for forming non-random patterns of energy relay materials with energy localization properties.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Application claims the benefit of priority to U.S. Provisional Patent Application No. 62/617,288, entitled “System and Methods for Transverse Energy Localization in Energy Relays Using Ordered Structures,” filed Jan. 14, 2018, and to U.S. Provisional Patent Application No. 62/617,293, entitled “Novel Application of Holographic and Light Field Technology,” filed Jan. 14, 2018, which are both herein incorporated by reference in their entirety.

TECHNICAL FIELD

This disclosure generally relates to light field energy systems, and more specifically, to systems of transverse localization of energy in energy relays using non-random arrangements of relay materials as well as methods of manufacturing energy relays thereof.

BACKGROUND

The dream of an interactive virtual world within a “holodeck” chamber as popularized by Gene Roddenberry's Star Trek and originally envisioned by author Alexander Moszkowski in the early 1900s has been the inspiration for science fiction and technological innovation for nearly a century. However, no compelling implementation of this experience exists outside of literature, media, and the collective imagination of children and adults alike.

SUMMARY

Disclosed are systems and methods for manufacturing energy relays for energy directing systems inducing Ordered Energy Localization effects. Energy relay materials comprising non-random patterns of energy relay materials, and criteria for forming such, are disclosed. Transverse planar as well as multi-dimensional energy relay material configurations are discussed. Methods and systems are disclosed for forming energy relay materials with Ordered Energy Localization properties.

In an embodiment, an energy relay comprises: a plurality of modules assembled in a structure, each module comprising first component engineered structures and second component engineered structures; wherein each module in the structure comprises an arrangement of the first and second component engineered structures in a substantially non-random pattern in a transverse plane of the energy relay; wherein the first and second component engineered structures are configured to cooperate to transport energy along a longitudinal plane that is normal to the transverse plane; the energy relay having substantially higher energy transport efficiency in the longitudinal plane than in the transverse plane.

In an embodiment, an energy relay comprises: a plurality of first and second component engineered structures, each comprising a cross-sectional shape of a set of one or more shapes along a transverse plane of the energy relay; wherein the plurality of first and second component engineered structures are substantially arranged in a tiling across the transverse plane of the energy relay; wherein the energy relay has substantially higher energy transport efficiency along a longitudinal plane than along the transverse plane.

In an embodiment, an energy relay comprises: a plurality of volumetric structures, each comprising one or more component engineered structures, and configured to tessellate volumetrically; wherein the plurality of volumetric structures are located in an assembly substantially according to a three-dimensional tessellation of the volumetric structures, the assembly being configured to transport energy in a longitudinal direction therethrough and having substantially higher transport efficiency in the longitudinal direction than in a transverse direction, normal to the longitudinal direction; wherein the plurality of volumetric structures are configured to tessellate volumetrically such that there is at least one substantially linear path through the volumetric tessellation, the substantially linear path substantially coinciding with only similar component engineered structures, and oriented substantially along the longitudinal direction.

In an embodiment, a method for forming an energy relay comprises: providing a plurality of first component engineered structures and a plurality of second component engineered structures; and forming a first arrangement of the pluralities of first and second component engineered structures comprising a substantially non-random pattern of the first and second component engineered structures in a transverse plane of the energy relay; and repeating at least the following steps until the arrangement has desired engineered properties, the steps including: processing the first arrangement of first and second component engineered structures into an assembly; and heating at least a first portion of the assembly, the formed energy relay having a first transverse dimension prior to being heated, and applying a tensile force longitudinally along at least the first portion of the heated assembly, thereby altering the first portion to have a second transverse dimension, narrower than the first transverse dimension, while substantially maintaining the substantially non-random pattern of first and second component engineered structures in the transverse plane; and forming a second arrangement of a plurality of substantially similar altered first portions, where this second arrangement may be used in, place of the first arrangement for further iterations of the preceding processing, heating, and applying steps.

In an embodiment, a method for forming an energy relay comprises: providing a plurality of first component engineered structures and a plurality of second component engineered structures; and forming an arrangement of the first and second component engineered structures comprising a substantially non-random pattern of the first and second component engineered structures in a transverse plane of the energy relay; and wherein the arrangement of first and second component engineered structures is configured to transport energy along a longitudinal plane that is normal to the transverse plane, the arrangement having substantially higher energy transport efficiency in the longitudinal plane than in the transverse plane.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating design parameters for an energy directing system;

FIG. 2 is a schematic diagram illustrating an energy system having an active device area with a mechanical envelope;

FIG. 3 is a schematic diagram illustrating an energy relay system;

FIG. 4 is a schematic diagram illustrating an embodiment of energy relay elements adhered together and fastened to a base structure,

FIG. 5A is a schematic diagram illustrating an example of a relayed image through multi-core optical fibers;

FIG. 5B is a schematic diagram illustrating an example of a relayed image through an optical relay that exhibits the properties of the Transverse Anderson Localization principle,

FIG. 6 is a schematic diagram showing rays propagated from an energy surface to a viewer;

FIG. 7A illustrates a cutaway view of a flexible energy relay which achieves Transverse Anderson Localization by intermixing two component materials within an oil or liquid, in accordance with one embodiment of the present disclosure;

FIG. 7B illustrates a schematic cutaway view of a rigid energy relay which achieves Transverse Anderson Localization by intermixing two component materials within a bonding agent, and in doing so, achieves a path of minimum variation in one direction for one material property, in accordance with one embodiment of the present disclosure;

FIG. 8 illustrates a schematic cutaway view in the transverse plane the inclusion of a dimensional extra mural absorption (“DEMA”) material in the longitudinal direction designed to absorb energy, in accordance with one embodiment of the present disclosure;

FIG. 9 illustrates a schematic cutaway view in the transverse plane of a portion of an energy relay comprising a random distribution of two component materials;

FIG. 10 illustrates a schematic cutaway view in the transverse plane of a module of an energy relay comprising a non-random pattern of three component materials which define a single module;

FIG. 11 illustrates a. schematic cutaway view in the transverse plane of a portion of a pre fused energy relay comprising a random distribution of two component materials;

FIG. 12A illustrates a schematic cutaway view in the transverse plane of a portion of a pre-fused energy relay comprising a nonrandom distribution of three component materials which define multiple modules with similar orientations;

FIG. 12B illustrates a schematic cutaway view in the transverse plane of a portion of a pre-fused energy relay comprising, a non-random pattern of three component materials which define multiple modules with varying orientations,

FIG. 13 illustrates a schematic cutaway view in the transverse plane of a portion of a fused energy relay comprising a random distribution of two component materials;

FIG. 14 illustrates a schematic cutaway view in the transverse plane of a portion of a fused energy relay comprising a non-random pattern of three component materials;

FIG. 15 illustrates a schematic cross-sectional view of a portion of an energy relay comprising a randomized distribution of two different component engineered structure (“CES”) materials;

FIG. 16 illustrates a schematic cross-sectional view of a portion of an energy relay comprising a non-random pattern of three different CES materials;

FIG. 17 illustrates a schematic cross-sectional perspective view of a portion of an energy relay comprising a randomized distribution of aggregated particles of two component materials;

FIG. 18 illustrates a schematic cross-sectional perspective view of a portion of an energy relay comprising a non-random pattern of aggregated particles of three component materials;

FIG. 19 illustrates a schematic cutaway view in the transverse plane of a portion of a pre-fused energy relay comprising a non-random pattern of particles arranged in one of two module structures;

FIG. 20A illustrates a perspective view illustration of a pre-fused arrangement of three different CES particles in a non-random pattern with variable particle size;

FIG. 20B illustrates a perspective view illustration of a fused arrangement of three different CES particles in a non-random pattern;

FIG. 20C illustrates a schematic cutaway view in the transverse plane of a portion of a pre-fused energy relay comprising a non-random pattern of particles and additional energy inhibiting structures;

FIG. 20D illustrates a schematic cutaway view in the transverse plane of a portion of a fused energy relay comprising a non-random pattern of particles and additional energy inhibiting structures;

FIG. 20E illustrates a perspective view of a module of a pre-fused energy relay comprising a non-random pattern of hexagonally shaped particles;

FIG. 20F illustrates a perspective view of a module of a fused energy relay comprising a non-random pattern of hexagonally shaped particles;

FIG. 20G illustrates a perspective view of a module of a pre-fused energy relay comprising a non-random pattern of irregularly shaped CES regions

FIG. 20H illustrates a perspective cross-sectional view of a portion of a pre-fused tube and pellet system for manufacturing an energy relay;

FIG. 20I illustrates a perspective cross-sectional view of a portion of a fused tube and pellet system for manufacturing an energy relay;

FIG. 20J illustrates a schematic cutaway view in the transverse plane of a module of a pre-fused energy relay comprising a non-random pattern of particles of three component materials;

FIG. 20K illustrates a schematic cutaway view in the transverse plane of a portion of a pre-fused energy relay comprising a non-random pattern of particles of three component materials and a surrounding energy inhibiting material;

FIG. 21A illustrates a cross-sectional view in the transverse plane of a pre-fused energy relay comprising a flexible outer enclosure, end caps, and pellets of energy transport material arranged in a non-random pattern;

FIG. 21B illustrates a cross-sectional view of a fused version of a flexible relay;

FIG. 21C illustrates a cross sectional view of a flexible relay in a non-fused and non-flexed state;

FIG. 21D illustrates a schematic cross-sectional view of a flexible relay in a fused and non-flexed state;

FIG. 22A illustrates a schematic cutaway view in the transverse plane of a non-random pattern energy relay prior to fusing;

FIG. 22B illustrates a schematic cutaway view in the transverse plane of a formed non-random pattern energy relay after fusing, include original and reduced transverse dimension configurations.

FIG. 23 illustrates an embodiment for forming non-random pattern energy relays with a reduced transverse dimension;

FIG. 24 illustrates a block diagram of a process for heating and pulling relay materials into microstructure materials;

FIG. 25 illustrates an embodiment for forming non-random pattern energy relays with a reduced transverse dimension;

FIG. 26A illustrates an embodiment for fusing energy relay materials by fixing the pre-fused relay materials in a fixture;

FIG. 26B illustrates a perspective view of an assembled fixture containing energy relay materials as part of a process of relaxing and fusing the energy relay materials;

FIG. 26C illustrates a perspective view of an assembled fixture containing energy relay materials after the materials have fused together, to form the fused ordered energy relay material.

FIG. 26D illustrates a perspective view of an embodiment of an adjustable fixture for fusing energy relay materials;

FIG. 26E illustrates a cross-sectional view of the adjustable fixture in FIG. 26D,

FIG. 27 illustrates a block diagram of a process for forming an energy relay;

FIG. 28 illustrates a perspective view of a fused structure of energy relay materials having a non-random pattern,

FIG. 29A and FIG. 29B illustrate an embodiment of a device for manufacturing microstructure energy relay materials using a rotational drum method;

FIG. 30-FIG. 58G illustrate various tiling configurations for arranging energy relay materials into non-random patterns;

FIG. 59 illustrates a perspective view of a deconstructed assembly of ordered pyramids comprising three different CES materials;

FIG. 60 illustrates a perspective view of a partially deconstructed configuration of an assembly of ordered pyramids,

FIG. 61 illustrates a perspective view of an expanded assembly of ordered pyramids comprising three different CES materials;

FIG. 62 illustrates a perspective view of an assembled ordered volumetric structure;

FIG. 63 illustrates a perspective view of a plurality of the ordered volumetric structures in geometric tessellation;

FIG. 64 illustrates a perspective view of an assembly comprising additional ordered volumetric structures;

FIG. 65A illustrates a cross-sectional view in the transverse direction of an assembly of ordered volumetric structures of energy relay material;

FIG. 65B illustrates across-sectional view in the longitudinal direction of an assembly of ordered volumetric structures of energy relay material;

FIG. 66A illustrates an embodiment of a volumetric structure comprising three different substructures;

FIG. 66B illustrates an embodiment of a volumetric structure comprising two different sub structures;

FIG. 66C illustrates an embodiment of a volumetric structure comprising three different substructures;

FIGS. 67A-C illustrate the assembly of several different volumetric structures having differently shaped substructures;

FIGS. 68A-F illustrate further embodiments of volumetric structures having different substructure components, as well as wire models illustrating the internal structure of certain volumetric structure embodiments;

FIG. 69A illustrates an embodiment of a plurality of volumetric structures arranged in an assembly, while FIGS. 69B and 69C illustrate cross sectional views of the assembly shown in FIG. 69A along the longitudinal and transverse directions, respectively;

FIG. 70A illustrates an embodiment of a plurality of volumetric structures arranged in an assembly, while FIGS. 70B and 70C illustrates cross sectional views of the assembly shown in FIG. 70A along the longitudinal and transverse directions, respectively;

FIG. 71 illustrates an embodiment of an assembly of two different volumetric structures, wherein a first volumetric structure is configured to tessellate at the vertices of a plurality of larger second volumetric structures;

FIG. 72 illustrates a tapered energy relay mosaic arrangement;

FIG. 73 illustrates a side view of an energy relay element stack comprising of two compound optical relay tapers in series;

FIG. 74 is a schematic diagram demonstrating the fundamental principles of internal reflection;

FIG. 75 is a schematic diagram demonstrating a light ray entering, an optical fiber, and the resulting conical light distribution at the exit of the relay;

FIG. 76 illustrates an optical taper relay configuration with a 3:1 magnification factor and the resulting viewed angle of light of an attached energy source, in accordance with one embodiment of the present disclosure;

FIG. 77 illustrates an optical taper relay with a curved surface on the energy source side of the optical taper relay resulting in the increased overall viewing angle of the energy source, in accordance with one embodiment of the present disclosure;

FIG. 78 illustrates an optical taper relay with a non-perpendicular but planar surface on the energy source side, in accordance with one embodiment of the present disclosure;

FIG. 79 illustrates an optical taper relay and illumination cones of a taper with a concave surface on the side of the energy source;

FIG. 80 illustrates an optical taper relay and light illumination cones with the same convex surface on the side of the energy source, but with a concave output energy surface geometry, in accordance with one embodiment of the present disclosure;

FIG. 81 illustrates multiple optical taper modules coupled together with curved energy source side surfaces to form an energy source viewable image from a perpendicular energy source surface, in accordance with one embodiment of the present disclosure;

FIG. 82 illustrates multiple optical taper modules coupled together with perpendicular energy source side geometries and a convex energy source surface radial about a center axis, in accordance with one embodiment of the present disclosure;

FIG. 83 illustrates multiple optical taper relay modules coupled together with perpendicular energy source side geometries and a convex energy source side surface radial about a center axis, in accordance with one embodiment of the present disclosure;

FIG. 84 illustrates multiple optical taper relay modules with each energy source independently configured such that the viewable output rays of light are more uniform as viewed at the energy source, in accordance with one embodiment of the present disclosure;

FIG. 85 illustrates multiple optical taper relay modules where both the energy source side and the energy source are configured with various geometries to provide control over the input and output rays of light, in accordance with one embodiment of the present disclosure; and

FIG. 86 illustrates arrangement of multiple optical taper relay modules whose individual output energy surfaces have been ground to form a seamless concave cylindrical energy source which surrounds the viewer, with the source ends of the relays flat and each bonded to an energy source.

DETAILED DESCRIPTION

An embodiment of a Holodeck (collectively called “Holodeck Design Parameters”) provide sufficient energy stimulus to fool the human sensory receptors into believing that received energy impulses within a virtual, social and interactive environment are real, providing: 1) binocular disparity without external accessories, head-mounted eyewear, or other peripherals; 2) accurate motion parallax, occlusion and opacity throughout a viewing volume simultaneously for any number of viewers; 3) visual focus through synchronous convergence, accommodation and miosis of the eye for all perceived rays of light; and 4) converging energy wave propagation of sufficient density and resolution to exceed the human sensory “resolution” for vision, hearing, touch, taste, smell, and/or balance.

Based upon conventional technology to date, we are decades, if not centuries away from a technology capable of providing for all receptive fields in a compelling way as suggested by the Holodeck Design Parameters including the visual, auditory, somatosensory, gustatory, olfactory, and vestibular systems.

In this disclosure, the terms light field and holographic may be used interchangeably to define the energy propagation for stimulation of any sensory receptor response. While initial disclosures may refer to examples of electromagnetic and mechanical energy propagation through energy surfaces for holographic imagery and volumetric haptics, all forms of sensory receptors are envisioned in this disclosure. Furthermore, the principles disclosed herein for energy propagation along propagation paths may be applicable to both energy emission and energy capture.

Many technologies exist today that are often unfortunately confused with holograms including lenticular printing, Pepper's Ghost, glasses-free stereoscopic displays, horizontal parallax displays, head-mounted VR and AR displays (HMD), and other such illusions generalized as “fauxlography.” These technologies may exhibit some of the desired properties of a true holographic display, however, lack the ability to stimulate the human visual sensory response in any way sufficient to address at least two of the four identified Holodeck Design Parameters.

These challenges have not been successfully implemented by conventional technology to produce a seamless energy surface sufficient for holographic energy propagation There are various approaches to implementing volumetric and direction multiplexed light field displays including parallax barriers, hogels, voxels, diffractive optics, multi-view projection, holographic diffusers, rotational mirrors, multilayered displays, time sequential displays, head mounted display, etc., however, conventional approaches may involve a compromise on image quality, resolution, angular sampling density, size, cost, safety, frame rate, etc., ultimately resulting in an unviable technology.

To achieve the Holodeck Design Parameters for the visual, auditory, somatosensory systems, the human acuity of each of the respective systems is studied and understood to propagate energy waves to sufficiently fool the human sensory receptors. The visual system is capable of resolving to approximately 1 arc min, the auditory system may distinguish the difference in placement as little as three degrees, and the somatosensory systems at the hands are capable of discerning points separated by 2-12rnm While there are various and conflicting ways to measure these acuities, these values are sufficient to understand the systems and methods to stimulate perception of energy propagation

Of the noted sensory receptors, the human visual system is by far the most sensitive given that even a single photon can induce sensation. For this reason, much of this introduction will focus on visual energy wave propagation, and vastly lower resolution energy systems coupled within a disclosed energy waveguide surface may converge appropriate signals to induce holographic sensory perception. Unless otherwise noted, all disclosures apply to all energy and sensory domains.

When calculating for effective design parameters of the energy propagation for the visual system given a viewing volume and viewing distance, a desired energy surface may be designed to include many gigapixels of effective energy location density. For wide viewing volumes, or near field viewing, the design parameters of a desired energy surface may include hundreds of gigapixels or more of effective energy location density. By comparison, a desired energy source may be designed to have 1 to 250 effective megapixels of energy location density for ultrasonic propagation of volumetric haptics or an array of 36 to 3,600 effective energy locations for acoustic propagation of holographic sound depending on input environmental variables. What is important to note is that with a disclosed bi-directional energy surface architecture, all components may be configured to form the appropriate structures for any energy domain to enable holographic propagation.

However, the main challenge to enable the Holodeck today involves available visual technologies and electromagnetic device limitations. Acoustic and ultrasonic devices are less challenging given the orders of magnitude difference in desired density based upon sensory acuity in the respective receptive field, although the complexity should not be underestimated. While holographic emulsion exists with resolutions exceeding the desired density to encode interference patterns in static imagery, state-of-the-art display devices are limited by resolution, data throughput and manufacturing feasibility. To date, no singular display device has been able to meaningfully produce a light field having near holographic resolution for visual acuity.

Production of a single silicon-based device capable of meeting the desired resolution for a compelling light field display may not practical and may involve extremely complex fabrication processes beyond the current manufacturing capabilities The limitation to tiling multiple existing display devices together involves the seams and gap formed by the physical size of packaging, electronics, enclosure, optics and a number of other challenges that inevitably result in an unviable technology from an imaging, cost and/or a size standpoint.

The embodiments disclosed herein may provide a real-world path to building the Holodeck

Example embodiments will now be described hereinafter with, reference to the accompanying drawings, which form a part hereof, and which illustrate example embodiments which may be practiced. As used in the disclosures and the appended claims, the terms “embodiment”, “example embodiment”, and “exemplary embodiment” do not necessarily refer to a single embodiment, <although they may, and various example embodiments may be readily combined and interchanged, without departing from the scope or spirit of example embodiments. Furthermore, the terminology as used herein is for the purpose of describing example embodiments only and is not intended to be limitations. In this respect, as used herein, the term “in” may include “in” and “on”, and the terms “a,” “an” and “the” may include singular and plural references. Furthermore, as used herein, the term “by” may also mean “from”, depending on the context. Furthermore, as used herein, the term “if” may also mean “when” or “upon,” depending on the context. Furthermore, as used herein, the words “and/or” may refer to and encompass any and all possible combinations of one or more of the associated listed items.

Holographic System Considerations: Overview ofLight Field Energy Propagation Resolution

Light field and holographic display is the result of a plurality of projections where energy surface locations provide angular, color and intensity information propagated within a viewing volume. The disclosed energy surface provides opportunities for additional information to coexist and propagate through the same surface to induce other sensory system responses. Unlike a stereoscopic display, the viewed position of the converged energy propagation paths in space do not vary as the viewer moves around the viewing volume and any number of viewers may simultaneously see propagated objects in real-world space as if it was truly there. In some embodiments, the propagation of energy may be located in the same energy propagation path but in opposite directions. For example, energy emission and energy capture along an energy propagation path are both possible in some embodiments of the present disclosed.

FIG. 1 is a schematic diagram illustrating variables relevant for stimulation of sensory receptor response. These variables may include surface diagonal 101, surface width 102, surface height 103, a determined target seating distance 118, the target seating field of view field of view from the center of the display 104, the number of intermediate samples demonstrated here as samples between the eyes 105, the average adult inter-ocular separation 106, the average resolution of the human eye in arcmin 107, the horizontal field of view formed between the target viewer location and the surface width 108, the vertical field of view formed between the target viewer location and the surface height 109, the resultant horizontal waveguide element resolution, or total number of elements, across the surface 110, the resultant vertical waveguide element resolution, or total number of elements, across the surface 111, the sample distance based upon the inter-ocular spacing between the eyes and the number of intermediate samples for angular projection between the eyes 112, the angular sampling may be based upon the sample distance and the target seating distance 113, the total resolution Horizontal per waveguide element derived from the angular sampling desired 114, the total resolution Vertical per waveguide element derived from the angular sampling desired 115, device Horizontal is the count of the determined number of discreet energy sources desired 116, and device Vertical is the count of the determined number of discreet energy sources desired 117

A method to understand the desired minimum resolution may be based upon the following criteria to ensure sufficient stimulation of visual (or other) sensory receptor response: surface size (e g., 84″ diagonal), surface aspect ratio (e g., 16:9), seating distance (e g., 128″ from the display), seating field of view (e.g., 120 degrees or +/−60 degrees about the center of the display), desired intermediate samples at a distance (e.g., one additional propagation path between the eyes), the average inter-ocular separation of an adult (approximately 65 mm), and the average resolution of the human eye (approximately 1 arcmin). These example values should be considered placeholders depending on the specific application design parameters.

Further, each of the values attributed to the visual sensory receptors may be replaced with other systems to determine desired propagation path parameters. For other energy propagation embodiments, one may consider the auditory system's angular sensitivity as low as three degrees and the somatosensory system's spatial resolution of the hands as small as 2-12 mm.

While there are various and conflicting ways to measure these sensory acuities, these values are sufficient to understand the systems and methods to stimulate perception of virtual energy propagation. There are many ways to consider the design resolution, and the below proposed methodology combines pragmatic product considerations with the biological resolving limits of the sensory systems. As will be appreciated by one of ordinary skill in the art, the following overview is a simplification of any such system design, and should be considered for exemplary purposes only

With, the resolution limit of the sensory system understood, the total energy waveguide element density may be calculated such that the receiving sensory system cannot discern a single energy waveguide element from an adjacent element, given:

${{Surface}\mspace{14mu}{Aspect}\mspace{14mu}{Ratio}} = \frac{{Width}\mspace{14mu}(W)}{{Height}\mspace{14mu}(H)}$ ${{Surface}\mspace{14mu}{Horizontal}\mspace{14mu}{Size}} = {{Surface}\mspace{14mu}{Diagonal}*\left( \frac{1}{\sqrt{\left( {1 + \left( \frac{H}{W} \right)^{2}} \right.}} \right)}$ ${{Surface}\mspace{14mu}{Vertical}\mspace{14mu}{Size}} = {{Surface}\mspace{14mu}{Diagonal}*\left( \frac{1}{\sqrt{\left( {1 + \left( \frac{W}{H} \right)^{2}} \right.}} \right)}$ ${{Horizontal}\mspace{14mu}{Field}\mspace{14mu}{of}\mspace{14mu}{View}} = {2*{{atan}\left( \frac{{Surface}\mspace{14mu}{Horizontal}\mspace{14mu}{Size}}{2*{Seating}\mspace{14mu}{Distance}} \right)}}$ ${{Vertical}\mspace{14mu}{Field}\mspace{14mu}{of}\mspace{14mu}{View}} = {2*{{atan}\left( \frac{{Surface}\mspace{14mu}{Verticle}\mspace{14mu}{Size}}{2*{Seating}\mspace{14mu}{Distance}} \right)}}$ ${{Horizontal}\mspace{14mu}{Element}\mspace{14mu}{Resolution}} = {{Horizontal}\mspace{14mu}{FoV}*\frac{60}{{Eye}\mspace{14mu}{Resolution}}}$ ${{Vertical}\mspace{14mu}{Element}\mspace{14mu}{Resolution}} = {{Vertical}\mspace{14mu}{FoV}*\frac{60}{{Eye}\mspace{14mu}{Resolution}}}$

The above calculations result in approximately a 32×18° field of view resulting in approximately 1920×1080 (rounded to nearest format) energy waveguide elements being desired. One may also constrain the variables such that the field of view is consistent for both (u, v) to provide a more regular spatial sampling of energy locations (e g pixel aspect ratio) The angular sampling of the system assumes a defined target viewing volume location and additional propagated energy paths between two points at the optimized distance, given:

${{Sample}\mspace{14mu}{Distance}} = \frac{{Inter}\text{-}{Ocular}\mspace{14mu}{Distance}}{\left( {{{Number}\mspace{14mu}{of}\mspace{14mu}{Desired}\mspace{14mu}{Intermediate}\mspace{14mu}{Samples}} + 1} \right)}$ ${{Angular}\mspace{14mu}{Sampling}} = {{atan}\left( \frac{{Sample}\mspace{14mu}{Distance}}{{Seating}\mspace{14mu}{Distance}} \right)}$

In this case, the inter-ocular distance is leveraged to calculate the sample distance although any metric may be leveraged to account for appropriate number of samples as a given distance. With the above variables considered, approximately one ray per 0.57° may be desired and the total system resolution per independent sensory system may be determined, given:

${{Locations}\mspace{14mu}{Per}\mspace{14mu}{{Element}(N)}} = \frac{{Seating}\mspace{14mu}{FoV}}{{Angular}\mspace{14mu}{Sampling}}$ Total  Resolution  H = N * Horizontal  Element  Resolution Total  Resolution  V = N * Vertical  Element  Resolution

With the above scenario given the size of energy surface and the angular resolution addressed for the visual acuity system, the resultant energy surface may desirably include approximately 400k×225k pixels of energy resolution locations, or 90 gigapixels holographic propagation density. These variables provided are for exemplary purposes only and many other sensory and energy metrology considerations should be considered for the optimization of holographic propagation of energy. In an additional embodiment, 1 gigapixel of energy resolution locations may be desired based upon the input variables. In an additional embodiment, 1,000 gigapixels of energy resolution locations may be desired based upon the input variables.

Current Technology Limitations: Active Area, Device Electronics, Packaging, and the Mechanical Envelope

FIG. 2 illustrates a device 200 having an active area 220 with a certain mechanical form factor. The device 200 may include drivers 230 and electronics 240 for powering and interface to the active area 220, the active area having a dimension as shown by the x and y arrows. This device 200 does not take into account the cabling and mechanical structures to drive, power and cool components, and the mechanical footprint may be further minimized by introducing a flex cable into the device 200. The minimum footprint for such a device 200 may also be referred to as a mechanical envelope 210 having a dimension as shown by the M:x and M:y arrows. This device 200 is for illustration purposes only and custom electronics designs may further decrease the mechanical envelope overhead, but in almost all cases may not be the exact size of the active area of the device. In an embodiment, this device 200 illustrates the dependency of electronics as it relates to active image area 220 for a micro OLED; DLP chip or LCD panel, or any other technology with the purpose of image illumination.

In some embodiments, it may also be possible to consider other projection technologies to aggregate multiple images onto a larger overall display. However, this may come at the cost of greater complexity for throw distance, minimum focus, optical quality, uniform field resolution, chromatic aberration, thermal properties, calibration, alignment, additional size or form factor For most practical applications, hosting tens or hundreds of these projection sources 200 may result in a design that is much larger with less reliability.

For exemplary purposes only, assuming energy devices with an energy location density of 3840×2160 sites, one may determine the number of individual energy devices (e.g., device 100) desired for an energy surface, given:

${{Devices}\mspace{14mu} H} = \frac{{Total}\mspace{14mu}{Resolution}\mspace{14mu} H}{{Device}\mspace{14mu}{Resolution}\mspace{14mu} H}$ ${{Devices}\mspace{14mu} V} = \frac{{Total}\mspace{14mu}{Resolution}\mspace{14mu} V}{{Device}\mspace{14mu}{Resolution}\mspace{14mu} V}$

Given the above resolution considerations, approximately 105×105 devices similar to those shown in FIG. 2 may be desired. It should be noted that many devices may include various pixel structures that may or may not map to a regular grid. In the event that there are additional sub-pixels or locations within each full pixel, these may be exploited to generate additional resolution or angular density. Additional signal processing may be used to determine how to convert the light field into the correct (u,v) coordinates depending on the specified location of the pixel structure(s) and can be an explicit characteristic of each device that is known and calibrated. Further, other energy domains may involve a different handling of these ratios and device structures, and those skilled in the art will understand the direct intrinsic relationship between each of the desired frequency domains. This will be shown and discussed in more detail in subsequent disclosure.

The resulting calculation may be used to understand how many of these individual devices may be desired to produce a full resolution energy surface. In this case, approximately 105×105 or approximately 11,080 devices may be desired to achieve the visual acuity threshold. The challenge and novelty exists within the fabrication of a seamless energy surface from these available energy locations for sufficient sensory holographic propagation.

Summary of Seamless Energy Surfaces: Configurations and Designs for Arrays of Energy Relays

In some embodiments, approaches are disclosed to address the challenge of generating high energy location density from an array of individual devices without seams due to the limitation of mechanical structure for the devices. In an embodiment, an energy propagating relay system may allow for an increase in the effective size of the active device area to meet or exceed the mechanical dimensions to configure an array of relays and form a singular seamless energy surface.

FIG. 3 illustrates an embodiment of such an energy relay system 300. As shown, the relay system 300 may include a device 310 mounted to a mechanical envelope 320, with an energy relay element 330 propagating energy from the device 310. The relay element 330 may be configured to provide the ability to mitigate any gaps 340 that may be produced when multiple mechanical envelopes 320 of the device are placed into an array of multiple devices 310.

For example, if a device's active area 310 is 20 mm×10 mm and the mechanical envelope 320 is 40 mm×20 mm, an energy relay element 330 may be designed with a magnification of 2:1 to produce a tapered form that is approximately 20 mm×10 mm on a minified end (arrow A) and 40 mm×20 mm on a magnified end (arrow B), providing the ability to align an array of these elements 330 together seamlessly without altering or colliding with the mechanical envelope 320 of each device 310. Mechanically, the relay elements 330 may be bonded or fused together to align and polish ensuring minimal seam gap 340 between devices 310. In one such embodiment, it is possible to achieve a seam gap 340 smaller than the visual acuity limit of the eye.

FIG. 4 illustrates an example of a base structure 400 having energy relay elements 410 formed together and securely fastened to an additional mechanical structure 430. The mechanical structure of the seamless energy surface 420 provides the ability to couple multiple energy relay elements 410, 450 in series to the same base structure through bonding or other mechanical processes to mount relay elements 410, 450. In some embodiments, each relay element 410 may be fused, bonded, adhered, pressure fit, aligned or otherwise attached together to form the resultant seamless energy surface 420. In some embodiments, a device 480 may be mounted to the rear of the relay element 410 and aligned passively or actively to ensure appropriate energy location alignment within the determined tolerance is maintained.

In an embodiment, the seamless energy surface comprises one or more energy locations and one or more energy relay element stacks comprise a first and second side and each energy relay element stack is arranged to form a singular seamless display surface directing energy along propagation paths extending between one or more energy locations and the seamless display surface, and where the separation between the edges of any two adjacent second sides of the terminal energy relay elements is less than the minimum perceptible contour as defined by the visual acuity of a human eye having better than 20/40 vision at a distance greater than the width of the singular seamless display surface.

In an embodiment, each of the seamless energy surfaces comprise one or more energy relay elements each with one or more structures forming a first and second surface with a transverse and longitudinal orientation. The first relay surface has an area different than the second resulting in positive or negative magnification and configured with explicit surface contours for both the first and second surfaces passing energy through the second relay surface to substantially fill a +/−10-degree angle with respect to the normal of the surface contour across the entire second relay surface.

In an embodiment, multiple energy domains may be configured within a single, or between multiple energy relays to direct one or more sensory holographic energy propagation paths including visual, acoustic, tactile or other energy domains.

In an embodiment, the seamless energy surface is configured with energy relays that comprise two or more first sides for each second side to both receive and emit one or more energy domains simultaneously to provide bi-directional energy propagation throughout the system.

In an embodiment, the energy relays are provided as loose coherent elements.

Introduction to Component Engineered Structures: Disclosed Advances in Transverse Anderson Localization Energy Relays

The properties of energy relays may be significantly optimized according to the principles disclosed herein for energy relay elements that induce Transverse Anderson Localization Transverse Anderson Localization is the propagation of a ray transported through a transversely disordered but longitudinally consistent material.

This implies that the effect of the materials that produce the Anderson Localization phenomena may be less impacted by total internal reflection than by the randomization between multiple-scattering paths where wave interference can completely limit the propagation in the transverse orientation while continuing in the longitudinal orientation.

Of significant additional benefit is the elimination of the cladding of traditional multi-core optical fiber materials. The cladding is to functionally eliminate the scatter of energy between fibers, but simultaneously act as a barrier to rays of energy thereby reducing transmission by at least the core to clad ratio (e.g., a core to clad ratio of 70:30 will transmit at best 70% of received energy transmission) and additionally forms a strong pixelated patterning in the propagated energy.

FIG. 5A illustrates an end view of an example of one such non-Anderson Localization energy relay 500 wherein an image is relayed through multi-core optical fibers where pixilation and fiber noise may be exhibited due to the intrinsic properties of the optical fibers. With traditional multi-mode and multi-core optical fibers, relayed images may be intrinsically pixelated due to the properties of total internal reflection of the discrete array of cores where any cross-talk between cores will reduce the modulation transfer function and increase blurring. The resulting imagery produced with traditional multi-core optical fiber tends to have a residual fixed noise fiber pattern similar to those shown in FIG. 5A.

FIG. 5B, illustrates an example of the same relayed image 550 through an energy relay comprising materials that exhibit the properties of Transverse Anderson Localization, where the relayed pattern has a greater density grain structures as compared to the fixed fiber pattern from FIG. 5A. In an embodiment, relays comprising randomized microscopic component engineered structures induce Transverse Anderson Localization and transport light more efficiently with higher propagation of resolvable resolution than commercially available multi-mode glass optical fibers.

In an embodiment, a relay element exhibiting Transverse Anderson Localization may comprise a plurality of at least two different component engineered structures in each of three orthogonal planes arranged in a dimensional lattice and the plurality of structures form randomized distributions of material wave propagation properties in a transverse plane within the dimensional lattice and channels of similar values of material wave propagation properties in a longitudinal plane within the dimensional lattice, wherein energy waves propagating through the energy relay have higher transport efficiency in the longitudinal orientation versus the transverse orientation and are spatially localized in the transverse orientation.

In an embodiment, a randomized distribution of material wave propagation properties in a transverse plane within the dimensional lattice may lead to undesirable configurations due to the randomized nature of the distribution. A randomized distribution of material wave propagation properties may induce Anderson Localization of energy on average across the entire transverse plane, however limited areas of similar materials having similar wave propagation properties may form inadvertently as a result of the uncontrolled random distribution. For example, if the size of these local areas of similar wave propagation properties become too large relative to their intended energy transport domain, there may be a potential reduction in the efficiency of energy transport through the material

In an embodiment, a relay may be formed from a randomized distribution of component engineered structures to transport visible light of a certain wavelength range by inducing Transverse Anderson Localization of the light. However, due to their random distribution, the structures may inadvertently arrange such that a continuous area of a single component engineered structure forms across the transverse plane which is multiple times larger than the wavelength of visible light. As a result, visible light propagating along the longitudinal axis of the large, continuous, single-material region may experience a lessened Transverse Anderson Localization effect and may suffer degradation of transport efficiency through the relay

In an embodiment, it may be desirable to design a non-random pattern of material wave propagation properties in the transverse plane of an energy relay material. Such a non-random (or “ordered”) distribution would ideally induce an energy localization effect through methods similar to Transverse Anderson Localization, while minimizing potential reductions in transport efficiency due to abnormally distributed material properties inherently resulting from a random property distribution.Using a non-random pattern of material wave propagation properties to induce a transverse energy localization effect similar to that of Transverse Anderson Localization in an energy relay element will hereafter be referred to as Ordered Energy Localization.

In an embodiment, multiple energy domains may be configured within a single, or between multiple Ordered Energy Localization energy relays to direct one or more sensory holographic energy propagation paths including visual, acoustic, tactile or other energy domains.

In an embodiment, a seamless energy surface is configured with Ordered Energy Localization energy relays that comprise two or more first sides for each second side to both receive and emit one or more energy domains simultaneously to provide bi-directional energy propagation throughout the system.

In an embodiment, the Ordered Energy Localization energy relays are configured as loose coherent or flexible energy relay elements.

Considerations for 4D Plenoptic Functions: Selective Propagation of Energy through Holographic Waveguide Arrays

As discussed above and herein throughout, a light field display system generally includes an energy source (e.g., illumination source) and a seamless energy surface configured with sufficient energy location density as articulated in the above discussion. A plurality of relay elements may be used to relay energy from the energy devices to the seamless energy surface. Once energy has been delivered to the seamless energy surface with the requisite energy location density, the energy can be propagated in accordance with a 4D plenoptic function through a disclosed energy waveguide system. As will be appreciated by one of ordinary skill in the art, a 4D plenoptic function is well known in the art and will not be elaborated further herein

The energy waveguide system selectively propagates energy through a plurality of energy locations along the seamless energy surface representing the spatial coordinate of the 4D plenoptic function with a structure configured to alter an angular direction of the energy waves passing through representing the angular component of the 4D plenoptic function, wherein the energy waves propagated may converge in space in accordance with a plurality of propagation paths directed by the 4D plenoptic function.

Reference is now made to FIG. 6 illustrating an example of light field energy surface in 4D image space in accordance with a 4D plenoptic function. The figure shows ray traces of an energy surface 600 to a viewer 620 in describing how the rays of energy converge in space 630 from various positions within the viewing volume As shown, each waveguide element 610 defines four dimensions of information describing energy propagation 640 through the energy surface 600. Two spatial dimensions (herein referred to as x and y) are the physical plurality of energy locations that can be viewed in image space, and the angular components theta and phi (herein referred to as u and v), which is viewed in virtual space when projected through the energy waiveguide array. In general, and in accordance with a 4D plenoptic function, the plurality of waveguides (e g , lenslets) are able to direct an energy location from the x, y dimension to a unique location in virtual space, along a direction defined by the u, v angular component, in forming the holographic or light field system described herein.

However, one skilled in the art will understand that a significant challenge to light field and holographic display technologies arises from uncontrolled propagation of energy due to designs that have not accurately accounted for any of diffraction, scatter, diffusion, angular direction, calibration, focus, collimation, curvature, uniformity, element cross-talk, as well as a multitude of other parameters that contribute to decreased effective resolution as well as an inability to accurately converge energy with sufficient fidelity

In an embodiment, an approach to selective energy propagation for addressing challenges associated with holographic display may include energy inhibiting elements and substantially filling waveguide apertures with near-collimated energy into an environment defined by a 4D plenoptic function.

In an embodiment, an array of energy waveguides may define a plurality of energy propagation paths for each waveguide element configured to extend through and substantially fill the waveguide element's effective aperture in unique directions defined by a prescribed 4D function to a plurality of energy locations along a seamless energy surface inhibited by one or more elements positioned to limit propagation of each energy location to only pass through a single waveguide element.

In an embodiment, multiple energy domains may be configured within a single, or between multiple energy waveguides to direct one or more sensory holographic energy propagations including visual, acoustic, tactile or other energy domains.

In an embodiment, the energy waveguides and seamless energy surface are configured to both receive and emit one or more energy domains to provide bi-directional energy propagation throughout the system.

In an embodiment, the energy waveguides are configured to propagate non-linear or non regular distributions of energy, including non-transmitting void regions, leveraging digitally encoded, diffractive, refractive, reflective, grin, holographic, Fresnel, or the like waveguide configurations for any seamless energy surface orientation including wall, table, floor, ceiling, room, or other geometry based environments. In an additional embodiment, an energy waveguide element may be configured to produce various geometries that provide any surface profile and/or tabletop viewing allowing users to view holographic imagery from all around the energy surface in a 360-degree configuration.

In an embodiment, the energy waveguide array elements may be reflective surfaces and the arrangement of the elements may be hexagonal, square, irregular, semi-regular, curved, non-planar, spherical, cylindrical, tilted regular, tilted irregular, spatially varying and/or multi-layered.

For any component within the seamless energy surface, waveguide, or relay components may include, but not limited to, optical fiber, silicon, glass, polymer, optical relays, diffractive, holographic, refractive, or reflective elements, optical face plates, energy combiners, beam splitters, prisms, polarization elements, spatial light modulators, active pixels, liquid crystal cells, transparent displays, or any similar materials exhibiting Anderson localization or total internal reflection.

Realizing the Holodeck: Aggregation of Bi-directional Seamless Energy Surface Systems to Stimulate Human Sensory Receptors within Holographic Environments

It is possible to construct large-scale environments of seamless energy surface systems by tiling, fusing, bonding, attaching, and/or stitching multiple seamless energy surfaces together forming arbitrary sizes, shapes, contours or form-factors including entire rooms. Each energy surface system may comprise an assembly having a base structure, energy surface, relays, waveguide, devices, and electronics, collectively configured for bi-directional holographic energy propagation, emission, reflection, or sensing.

In an embodiment, an environment of tiled seamless energy systems are aggregated to form large seamless planar or curved walls including installations comprising up to all surfaces in a given environment, and configured as any combination of seamless, discontinuous planar, faceted, curved, cylindrical, spherical, geometric, or non-regular geometries.

In an embodiment, aggregated tiles of planar surfaces form wall-sized systems for theatrical or venue-based holographic entertainment. In an embodiment, aggregated tiles of planar surfaces cover a room with four to six walls including both ceiling and floor for cave-based holographic installations In an embodiment, aggregated tiles of curved surfaces produce a cylindrical seamless environment for immersive holographic installations. In an embodiment, aggregated tiles of seamless spherical surfaces form a holographic dome for immersive Holodeck-based experiences.

In an embodiment, aggregated tiles of seamless curved energy waveguides provide mechanical edges following the precise pattern along the boundary of energy inhibiting elements within the energy waveguide structure to bond, align, or fuse the adjacent tiled mechanical edges of the adjacent waveguide surfaces, resulting in a modular and seamless energy waveguide system.

In a further embodiment of an aggregated tiled environment, energy is propagated bi-directionally for multiple simultaneous energy domains In an additional embodiment, the energy surface provides the ability to both display and capture simultaneously from the same energy surface with waveguides designed such that light field data may be projected by an illumination source through the waveguide and simultaneously received through the same energy surface. In an additional embodiment, additional depth sensing and active scanning technologies may be leveraged to allow for the interaction between the energy propagation and the viewer in correct world coordinates. In an additional embodiment, the energy surface and waveguide are operable to emit, reflect or converge frequencies to induce tactile sensation or volumetric haptic feedback In some embodiments, any combination of bi-directional energy propagation and aggregated surfaces are possible.

In an embodiment, the system comprises an energy waveguide capable of bi-directional emission and sensing of energy through the energy surface with one or more energy devices independently paired with two-or-more-path energy combiners to pair at least two energy devices to the same portion of the seamless energy surface, or one or more energy devices are secured behind the energy surface, proximate to an additional component secured to the base structure, or to a location in front and outside of the FOV of the waveguide for off-axis direct or reflective projection or sensing, and the resulting energy surface provides for bi-directional transmission of energy allowing the waveguide to converge energy, a first device to emit energy and a second device to sense energy, and where the information is processed to perform computer vision related tasks including, but not limited to, 4D plenoptic eye and retinal tracking or sensing of interference within propagated energy patterns, depth estimation, proximity, motion tracking, image, color, or sound formation, or other energy frequency analysis In an additional embodiment, the tracked positions actively calculate and modify positions of energy based upon the interference between the bi-directional captured data and projection information.

In some embodiments, a plurality of combinations of three energy devices comprising an ultrasonic sensor, a visible electromagnetic display, and an ultrasonic emitting, device are configured together for each of three first relay surfaces propagating energy combined into a single second energy relay surface with each of the three first surfaces comprising engineered properties specific to each device's energy domain, and two engineered waveguide elements configured for ultrasonic and electromagnetic energy respectively to provide the ability to direct and converge each device's energy independently and substantially unaffected by the other waveguide elements that are configured for a separate energy domain

In some embodiments, disclosed is a calibration procedure to enable efficient manufacturing to remove system artifacts and produce a geometric mapping of the resultant energy surface for use with encoding/decoding technologies as well as dedicated integrated systems for the conversion of data into calibrated information appropriate for energy propagation based upon the calibrated configuration files.

In some embodiments, additional energy waveguides in series and one or more energy devices may be integrated into a system to produce opaque holographic pixels.

In some embodiments, additional waveguide elements may be integrated comprising energy inhibiting elements, beam-splitters, prisms, active parallax barriers or polarization technologies in order to provide spatial and/or angular resolutions greater than the diameter of the waveguide or for other super-resolution purposes.

In some embodiments, the disclosed energy system may also be configured as a wearable bi-directional device, such as virtual reality (VR) or augmented reality (AR). In other embodiments, the energy system may include adjustment optical element(s) that cause the displayed or received energy to be focused proximate to a determined plane in space for a viewer. In some embodiments, the waveguide array may be incorporated to holographic head-mounted-display. In other embodiments, the system may include multiple optical paths to allow for the viewer to see both the energy system and a real-world environment (e g , transparent holographic display). In these instances, the system may be presented as near field in addition to other methods.

In some embodiments, the transmission of data comprises encoding processes with selectable or variable compression ratios that receive an arbitrary dataset of information and metadata; analyze said dataset and receive or assign material properties, vectors, surface IDs, new pixel data forming a more sparse dataset, and wherein the received data may comprise: 2D, stereoscopic, multi-view, metadata, light field, holographic, geometry, vectors or vectorized metadata, and an encoder/decoder may provide the ability to convert the data in real-time or off-line comprising image processing for: 2D; 2D plus depth, metadata or other vectorized information; stereoscopic, stereoscopic plus depth, metadata or other vectorized information; multi-view; multi-view plus depth, metadata or other vectorized information, holographic; or light field content; through depth estimation algorithms, with or without depth metadata; and an inverse ray tracing methodology appropriately maps the resulting converted data produced by inverse ray tracing from the various 2D, stereoscopic, multi-view, volumetric, light field or holographic data into real world coordinates through a characterized 4D plenoptic function. In these embodiments, the total data transmission desired may be multiple orders of magnitudes less transmitted information than the raw light field dataset.

Tapered Energy Relays

In order to further solve the challenge of generating high resolution from an array of individual energy wave sources containing extended mechanical envelopes, the use of tapered energy relays can be employed to increase the effective size of each energy source. An array of tapered energy relays can be stitched together to form a singular contiguous energy surface, circumventing the limitation of mechanical requirements for those energy sources.

In an embodiment, the one or more energy relay elements may be configured to direct energy along propagation paths which extend between the one or more energy locations and the singular seamless energy surface.

For example, if an energy wave source's active area is 20 mm×10 mm and the mechanical envelope is 40 mm×20 mm, a tapered energy relay may be designed with a magnification of 2:1 to produce a taper that is 20 mm×10 mm (when cut) on the minified end and 40 mm×20 mm (when cut) on the magnified end, providing the ability to align an array of these tapers together seamlessly without altering or violating the mechanical envelope of each energy wave source.

FIG. 72 illustrates one such tapered energy relay mosaic arrangement 7400, in accordance with one embodiment of the present disclosure. In FIG. 72, the relay device 7400 may include two or more relay elements 7402, each relay element 7402 formed of one or more structures, each relay element 7402 having a first surface 7406, a second surface 7408, a transverse orientation (generally parallel to the surfaces 7406, 7408) and a longitudinal orientation (generally perpendicular to the surfaces 7406, 7408). The surface area of the first surface 7406 may be different than the surface area of the second surface 7408. For relay element 7402, the surface area of the first surface 7406 is less than the surface area of the second surface 7408 In another embodiment, the surface area of the first surface 7406 may be the same or greater than the surface area of the second surface 7408. Energy waves can pass from the first surface 7406 to the second surface 7408, or vice versa.

In FIG. 72, the relay element 7402 of the relay element device 7400 includes a sloped profile portion 7404 between the first surface 7406 and the second surface 7408. In operation, energy waves propagating between the first surface 7406 and the second surface 7408 may have a higher transport efficiency in the longitudinal orientation than in the transverse orientation, and energy waves passing through the relay element 7402 may result in spatial magnification or spatial de-magnification. In other words, energy waves passing through the relay element 7402 of the relay element device 7400 may experience increased magnification or decreased magnification. In an embodiment, energy may be directed through the one or more energy relay elements with zero magnification. In some embodiments, the one or more structures for forming relay element devices may include glass, carbon, optical fiber, optical film, plastic, polymer, or mixtures thereof.

In one embodiment, the energy waves passing through the first surface have a first resolution, while the energy waves passing through the second surface have a second resolution, and the second resolution is no less than about 50% of the first resolution. In another embodiment, the energy waves, while having a uniform profile when presented to the first surface, may pass through the second surface radiating in every direction with an energy density in the forward direction that substantially fills a cone with an opening angle of +/−10 degrees relative to the normal to the second surface, irrespective of location on the second relay surface.

In some embodiments, the first surface may be configured to receive energy from an energy wave source, the energy wave source including a mechanical envelope having a width different than the width of at least one of the first surface and the second surface.

In an embodiment, energy may be transported between first and second surfaces which defines the longitudinal orientation, the first and second surfaces of each of the relays extends generally along a transverse orientation defined by the first and second directions, where the longitudinal orientation is substantially normal to the transverse orientation. In an embodiment, energy waves propagating through the plurality of relays have higher transport efficiency in the longitudinal orientation than in the transverse orientation and are spatially localized in the transverse plane due to randomized refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation via, the principle of Transverse Anderson Localization. In some embodiments where each relay is constructed of multicore fiber, the energy waves propagating within each relay element may travel in the longitudinal orientation determined by the alignment of fibers in this orientation.

Mechanically, these tapered energy relays are cut and polished to a high degree of accuracy before being bonded or fused together in order to align them and ensure that the smallest possible seam gap between the relays. The seamless surface formed by the second surfaces of energy relays is polished after the relays are bonded. In one such embodiment, using an epoxy that is thermally matched to the taper material, it is possible to achieve a maximum seam gap of 50 mm. In another embodiment, a manufacturing process that places the taper array under compression and/or heat provides the ability to fuse the elements together. In another embodiment, the use of plastic tapers can be more easily chemically fused or heat-treated to create the bond without additional bonding. For the avoidance of doubt, any methodology may be used to bond the array together, to explicitly include no bond other than gravity and/ or force

In an embodiment, a separation between the edges of any two adjacent second surfaces of the terminal energy relay elements may be less than a minimum perceptible contour as defined by the visual acuity of a human eye having 20/40 vision at a distance from the seamless energy surface that is the lesser of a height of the singular seamless energy surface or a width of the singular seamless energy surface.

A mechanical structure may be preferable in order to hold the multiple components in a fashion that meets a certain tolerance specification. In some embodiments, the first and second surfaces of tapered relay elements can have any polygonal shapes including without limitation circular, elliptical, oval, triangular, square, rectangle, parallelogram, trapezoidal, diamond, pentagon, hexagon, and so forth In some examples, for non-square tapers, such as rectangular tapers for example, the relay elements may be rotated to have the minimum taper dimension parallel to the largest dimensions of the overall energy source. This approach allows for the optimization of the energy source to exhibit the lowest rejection of rays of light due to the acceptance cone of the magnified relay element as when viewed from center point of the energy source. For example, if the desired energy source size is 100 mm by 60 mm and each tapered energy relay is 20 mm by 10 mm, the relay elements may be aligned and rotated such that an array of 3 by 10 taper energy relay elements may be combined to produce the desired energy source size. Nothing here should suggest that an array with an alternative configuration of an array of 6 by 5 matrix, among other combinations, could not be utilized. The array comprising of a 3×10 layout generally will perform better than the alternative 6×5 layout.

Energy Relay Element Stacks

While the most simplistic formation of an energy source system comprises of an energy source bonded to a single tapered energy relay element, multiple relay elements may be coupled to form a single energy source module with increased quality or flexibility. One such embodiment includes a first tapered energy relay with the minified end attached to the energy source, and a second tapered energy relay connected to the first relay element, with the minified end of the second optical taper in contact with the magnified end of the first relay element, generating a total magnification equal to the product of the two individual taper magnifications. This is an example of an energy relay element stack comprising of a sequence of two or more energy relay elements, with each energy relay element comprising a first side and a second side, the stack relaying energy from the first surface of the first element to the second surface of the last element in the sequence, also named the terminal surface Each energy relay element may be configured to direct energy therethrough.

In an embodiment, an energy directing device comprises one or more energy locations and one or more energy relay element stacks. Each energy relay element stack comprises one or more energy relay elements, with each energy relay element comprising a first surface and a second surface. Each energy relay element may be configured to direct energy therethrough. In an embodiment, the second surfaces of terminal energy relay elements of each energy relay element stack may be arranged to form a singular seamless display surface. In an embodiment, the one or more energy relay element stacks may be configured to direct energy along energy propagation paths which extend between the one or more energy locations and the singular seamless display surfaces

FIG. 73 illustrates a side view of an energy relay element stack 7500 including two compound optical relay tapers 7502, 7504 in series, both tapers with minified ends facing an energy source surface 7506, in accordance with an embodiment of the present disclosure. In FIG. 73, the input numerical aperture (NA) is 1.0 for the input of taper 7504, but only about 0:16 for the output of taper 7502. Notice that the output numerical aperture gets divided by the total magnification of 6, which is the product of 2 for taper 7504, and 3 for taper 7502 One advantage of this approach is the ability to customize the first energy wave relay element to account for various dimensions of energy source without alteration of the second energy wave relay element. It additionally provides the flexibility to alter the size of the output energy surface without changing the design of the energy source or the first relay element. Also shown in FIG. 73 is the energy source 7506 and the mechanical envelope 7508 containing the energy source drive electronics.

In an embodiment, the first surface may be configured to receive energy waves from an energy source unit (e.g., 7506), the energy source unit including a mechanical envelope having a width different than the width of at least one of the first surface and the second surface. In one embodiment, the energy waves passing through the first surface may have a first resolution, while the energy waves passing through the second surface may have a second resolution, such that the second resolution is no less than about 50% of the first resolution. In another embodiment, the energy waves, while having a uniform profile when presented to the first surface, may pass through the second surface radiating in every direction with an energy density in the forward direction that substantially fills a cone with an opening angle of +/−10 degrees relative to the normal to the second surface, irrespective of location on the second relay surface

In one embodiment, the plurality of energy relay elements in the stacked configuration may include a plurality of faceplates (relays with unity magnification). In some embodiments, the plurality of faceplates may have different lengths or are loose coherent optical relays. In other embodiments, the plurality of elements may have sloped profile portions, where the sloped profile portions may be angled, linear, curved, tapered, faceted or aligned at a non-perpendicular angle relative to a normal axis of the relay element. In yet another embodiment, energy waves propagating through the plurality of relay elements have higher transport efficiency in the longitudinal orientation than in the transverse orientation and are spatially localized in the transverse orientation due to randomized refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation. In embodiments where each energy relay is constructed of multicore fiber, the energy waves propagating within each relay element may travel in the longitudinal orientation determined by the alignment of fibers in this orientation.

Optical Image Relay and Taper Elements

Extremely dense fiber bundles can be manufactured with a plethora of materials to enable light to be relayed with pixel coherency and high transmission. Optical fibers provide the guidance of light along transparent fibers of glass, plastic, or a similar medium. This phenomenon is controlled by a concept called total internal reflection. A ray of light will be totally internally reflected between two transparent optical materials with a different index of refraction when the ray is contained within the critical angle of the material and the ray is incident from the direction of the more dense material.

FIG. 74 demonstrates the fundamental principles of internal reflection through a core-clad relay 7600 having a maximum acceptance angle Ø 7608 (or NA of the material), core 7612 and clad 7602 materials with differing refractive indices, and reflected 7604 and refracted 7610 rays. In general, the transmission of light decreases by less than 0.001 percent per reflection and a fiber that is about 50 microns in diameter may have 3,000 reflections per foot, which is helpful to understand how efficient that light transmission may be as compared to other compound optical methodologies.

One can calculate the relationship between the angle of incidence (I) and the angle of refraction (R) with Snell's law:

${\frac{\sin\mspace{14mu}\theta_{I}}{\sin\mspace{14mu}\theta_{R}} = \frac{n_{2}}{n_{1}}},$

where n₁ is the index of refraction of air and n₂ as the index of refraction of the core material 7612.

One skilled at the art of fiber optics will understand the additional optical principles associated with light gathering power, maximum angle of acceptance, and other required calculations to understand how light travels through the optical fiber materials. It is important to understand this concept, as the optical fiber materials should be considered a relay of light rather than a methodology to focus light as will be described within the following embodiments.

Understanding the angular distribution of light that exits the optical fiber is important to this disclosure, and may not be the same as would be expected based upon the incident angle. Because the exit azimuthal angle of the ray 7610 tends to vary rapidly with the maximum acceptance angle 7608, the length and diameter of the fiber, as well as the other parameters of the materials, the emerging rays tend to exit the fiber as a conical shape as defined by the incident and refracted angles.

FIG. 75 demonstrates an optical fiber relay system 7704 and how a ray of light 7702 entering an optical fiber 7704 may exit in a conical shape distribution of light 7706 with a specific azimuthal angle Ø. This effect may be observed by shining a laser pointer through a fiber and view the output ray at various distances and angles on a surface. The conical shape of exit with a distribution of light across the entire conical region (e.g., not only the radius of the conical shape) which will be an important concept moving forward with the designs proposed.

The main source for transmission loss in fiber materials are cladding, length of material, and loss of light for rays outside of the acceptance angle. The cladding is the material that surrounds each individual fiber within the larger bundle to insulate the core and help mitigate rays of light from traveling between individual fibers. In addition to this, additional opaque materials may be used to absorb light outside of acceptance angle called extra mural absorption (EMA). Both materials can help improve viewed image quality in terms of contrast, scatter and a number of other factors, but may reduce the overall light transmission from entry to exit. For simplicity, the percent of core to clad can be used to understand the approximate transmission potential of the fiber, as this may be one of the reasons for the loss of light. In most materials, the core to clad ratio may be in the range of approximately about 50% to about 80%, although other types of materials may be available and will be explored in the below discussion.

Each fiber may be capable of resolving approximately 0.5 photographic line pairs per fiber diameter, thus when relaying pixels, it may be important to have more than a single fiber per pixel. In some embodiments, a dozen or so per pixel may be utilized, or three or more fibers may be acceptable, as the average resolution between each of the fibers helps mitigate the associate MTF loss, when leveraging these materials.

In one embodiment, optical fiber may be implemented in the form of a fiber optic faceplate A faceplate is a collection of single or multi, or multi-multi fibers, fused together to form a vacuum-tight glass plate. This plate can be considered a theoretically zero-thickness window as the image presented to one side of the faceplate may be transported to the external surface with high efficiency. Traditionally, these faceplates may be constructed with individual fibers with a pitch of about 6 microns or larger, although higher density may be achieved albeit at the effectiveness of the cladding material which may ultimately reduce contrast and image quality.

In some embodiments, an optical fiber bundle may be tapered resulting in a coherent mapping of pixels with different sizes and commensurate magnification of each surface For example, the magnified end may refer to the side of the optical fiber element with the larger fiber pitch and higher magnification, and the minified end may refer to the side of the optical fiber element with the smaller fiber pitch and lower magnification. The process of producing various shapes may involve heating and fabrication of the desired magnification, which may physically alter the original pitch of the optical fibers from their original size to a smaller pitch thus changing the angles of acceptance, depending on location on the taper and NA. Another factor is that the fabrication process can skew the perpendicularity of fibers to the flat surfaces. One of the challenges with a taper design, among others, is that the effective NA of each end may change approximately proportional to the percentage of magnification For example, a taper with a 2:1 ratio may have a minified end with a diameter of 10 mm and a magnified end with a diameter of 20 mm If the original material had an NA of 0.5 with a pitch of 10 microns, the minified end will, have an approximately effective NA of 1.0 and pitch of 5 microns. The resulting acceptance and exit angles may change proportionally as well. There is far more complex analysis that can be performed to understand the exacting results from this process and anyone skilled in the art will be able to perform these calculations For the purposes of this discussion, these generalizations are sufficient to understand the imaging implications as well as overall systems and methods.

Use of Flexible Energy Sources and Curved Energy Relay Surfaces

It may be possible to manufacture certain energy source technologies or energy projection technologies with curved surfaces. For example, in one embodiment, for a source of energy, a curved OLED display panel may be used. In another embodiment, for a source of energy, a focus-free laser projection system may be utilized. In yet another embodiment, a projection system with a sufficiently wide depth of field to maintain focus across the projected surface may be employed. For the avoidance of doubt, these examples are provided for exemplary purposes and in no way limit the scope of technological implementations for this description of technologies.

Given the ability for optical technologies to produce a steered cone of light based upon the chief ray angle (CRA) of the optical configuration, by leveraging a curved energy surface, or a curved surface that may retain a fully focused projected image with known input angles of light and respective output modified angles may provide a more idealized viewed angle of light.

In one such embodiment, the energy surface side of the optical relay element may be curved in a cylindrical, spherical, planar, or non-planar polished configuration (herein referred to as “geometry” or “geometric”) on a per module basis, where the energy source originates from one more source modules. Each effective light-emitting energy source has its own respective viewing angle that is altered through the process of deformation. Leveraging this curved energy source or similar panel technology allows for panel technology that may be less susceptible to deformation and a reconfiguration of the CRA or optimal viewing angle of each effective pixel.

FIG. 76 illustrates an optical relay taper configuration 7800 with a 3:1 magnification factor and the resulting viewed angle of light of an attached energy source, in accordance with one embodiment of the present disclosure. The optical relay taper has an input. NA of 1.0 with a 3:1 magnification factor resulting in an effective NA for output rays of approximately 0.33 (there are many other factors involved here, this is for simplified reference only), with planar and perpendicular surfaces on either end of the tapered energy relay, and an energy source attached to the minified end. Leveraging this approach alone, the angle of view of the energy surface may be approximately ⅓ of that of the input angle. For the avoidance of doubt, a similar configuration with an effective magnification of 1:1 (leveraging an optical faceplate or otherwise) may additionally be leveraged, or any other optical relay type or configuration.

FIG. 77 illustrates the same tapered energy relay module 7900 as that of FIG. 76 but now with a surface on an energy source side having a curved geometric configuration 7902 while a surface opposite an energy source side 7903 having a planar surface and perpendicular to an optical axis of the module 7900. With this approach, the input angles (e.g., see arrows near 7902) may be biased based upon this geometry, and the output angles (e g , see arrows near 7903) may be tuned to be more independent of location on the surface, different than that of FIG. 76, given the curved surface 7902 as exemplified in FIG. 77, although the viewable exit cone of each effective light emission source on surface 7903 may be less than the viewable exit cone of the energy source input on surface 7902. This may be advantageous when considering a specific energy surface that optimizes the viewed angles of light for wider or more compressed density of available rays of light.

In another embodiment, variation in output angle may be achieved by making the input energy surface 7902 convex in shape. If such a change were made, the output cones of light near the edge of the energy surface 7903 would turn in toward the center.

In some embodiments, the relay element device may include a curved energy surface In one example, both the surfaces of the relay element device may be planar. Alternatively, in other examples, one surface may be planar and the other surface may be non-planar, or vice versa. Finally, in another example, both the surfaces of the relay element device may be non-planar. In other embodiments, a non-planar surface may be a concave surface or a convex surface, among other non-planar configurations For example, both surfaces of the relay element may be concave. In the alternative, both surfaces may be convex. In another example, one surface may be concave and the other may be convex. It will be understood by one skilled in the art that multiple configurations of planar, non-planar, convex and concave surfaces are contemplated and disclosed herein.

FIG. 78 illustrates an optical relay taper 8000 with a non-perpendicular but planar surface 8002 on the energy source side, in accordance with another embodiment of the present disclosure To articulate the significant customizable variation in the energy source side geometries, FIG. 78 illustrates the result of simply creating a non-perpendicular but planar geometry for the energy source side for comparison to FIG. 77 and to further demonstrate the ability to directly control the input acceptance cone angle and the output viewable emission cone angles of light 1, 2, 3 that are possible with any variation in surface characteristics.

Depending on the application, it may also be possible to design an energy relay configuration with the energy source side of the relay remaining perpendicular to the optical axis that defines the direction of light propagation within the relay, and the output surface of the relay being non-perpendicular to the optical axis. Other configurations may have both the input energy source side and the energy output side exhibiting various non-perpendicular geometric configurations. With this methodology, it may be possible to further increase control over the input and output energy source viewed angles of light.

In some embodiments, tapers may also be non-perpendicular to the optical axis of the relay to optimize a particular view angle. In one such embodiment a single taper such as the one shown in FIG. 76 may be cut into quadrants by cuts parallel with the optical axis, with the large end and small end of the tapers cut into four equal portions. These four quadrants and then re-assembled with each taper quadrant rotated about the individual optical center axis by 180 degrees to have the minified end of the taper facing away from the center of the re-assembled quadrants thus optimizing the field of view. In other embodiments, non-perpendicular tapers may also be manufactured directly as well to provide increased clearance between energy sources on the minified end without increasing the size or scale of the physical magnified end. These and other tapered configurations are disclosed herein

FIG. 79 illustrates the optical relay and light illumination cones of FIG. 76 with a concave surface on the side of the energy source. In this case, the cones of output light are significantly more diverged near the edges of the output energy surface plane than if the energy source side were flat, in comparison with FIG. 76.

FIG. 80 illustrates the optical taper relay 8200 and light illumination cones of FIG. 79 with the same concave surface on the side of the energy source. In this example, the output energy surface 8202 has a convex geometry. Compared to FIG. 79, the cones of output light on the concave output surface 8202 are more collimated across the energy source surface due to the input acceptances cones and the exit cone of light produced from this geometric configuration. For the avoidance of doubt, the provided examples are illustrative only and not intended to dictate explicit surface characteristics, since any geometric configuration for the input energy source side and the output energy surface may be employed depending on the desired angle of view and density of light for the output energy surface, and the angle of light produced from the energy source itself.

In some embodiments, multiple relay elements may be configured in series. In one embodiment, any two relay elements in series may additionally be coupled together with intentionally distorted parameters such that the inverse distortions from one element in relation to another help optically mitigate any such artifacts. In another embodiment, a first optical taper exhibits optical barrel distortions, and a second optical taper may be manufactured to exhibit the inverse of this artifact, to produce optical pin cushion distortions, such than when aggregated together, the resultant information either partially or completely cancels any such optical distortions introduced by any one of the two elements. This may additionally be applicable to any two or more elements such that compound corrections may be applied in series.

In some embodiments, it may be possible to manufacturer a single energy source board, electronics, and/or the like to produce an array of energy sources and the like in a small and/or lightweight form factor. With this arrangement, it may be feasible to further incorporate an optical relay mosaic such that the ends of the optical relays align to the energy source active areas with an extremely small form factor by comparison to individual components and electronics. Using this technique, it may be feasible to accommodate small form factor devices like monitors, smart phones and the like

FIG. 81 illustrates an assembly 8300 of multiple optical taper relay modules 8304, 8306, 8308, 8310, 8312 coupled together with curved energy source side surfaces 8314, 8316, 8318, 8320, 8322, respectively, to form an optimal viewable image 8302 from a plurality of perpendicular output energy surfaces of each taper, in accordance with one embodiment of the present disclosure. In this instance, the taper relay modules 8304, 8306, 8308, 8310, 8312 are formed in parallel. Although only a single row of taper relay modules is shown, in some embodiments, tapers with a stacked configuration may also be coupled together in parallel and in a row to form a contiguous, seamless viewable image 8302.

In FIG. 81, each taper relay module may operate independently or be designed based upon an array of optical relays. As shown in this figure, five modules with optical taper relays 8304, 8306, 8308, 8310, 8312 are aligned together producing a larger optical taper output energy surface 8302. In this configuration, the output energy surface 8302 may be perpendicular to the optical axis of each relay, and each of the five energy source sides 8314, 8316, 8318, 8320, 8322 may be deformed in a circular contour about a center axis that may lie in front of the output energy surface 8302, or behind this surface, allowing the entire array to function as a single output energy surface rather than as individual modules. It may additionally be possible to optimize this assembly structure 8300 further by computing the output viewed angle of light and determining the ideal surface characteristics required for the energy source side geometry. FIG. 81 illustrates one such embodiment where multiple modules are coupled together and the energy source side curvature accounts for the larger output energy surface viewed angles of light. Although five relay modules 8304, 8306, 8308, 8310, and 8312 are shown, it will be appreciated by one skilled in the art that more or fewer relay modules may be coupled together depending on the application, and these may be coupled together in two dimensions to form an arbitrarily large output energy surface 8302.

In one embodiment, the system of FIG. 81 includes a plurality of relay elements 8304, 8306, 8308, 8310, 8312 arranged across first and second directions (e g , across a row or in stacked configuration), where each of the plurality of relay elements extends along a longitudinal orientation between first and second surfaces of the respective relay element. In some embodiments, the first and second surfaces of each of the plurality of relay elements extends generally along a transverse orientation defined by the first and second directions, wherein the longitudinal orientation is substantially normal to the transverse orientation. In other embodiments, randomized refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation results in energy waves having substantially higher transport efficiency along the longitudinal orientation, and spatial localization along the transverse orientation.

In one embodiment, the plurality of relay elements may be arranged across the first direction or the second direction to form a single tiled surface along the first direction or the second direction, respectively. In some embodiments, the plurality of relay elements are arranged in a matrix having at least a 2×2 configuration, or in other matrices including without limitation a 3×3 configuration, a 4×4 configuration, a 3×10 configuration, and other configurations as can be appreciated by one skilled in the art. In other embodiments, seams between the single tiled surface may be imperceptible at a viewing distance of twice a minimum dimension of the single tiled surface.

In some embodiments, each of the plurality of relay elements (e.g. 8304, 8306, 8308, 8310, 8312) have randomized refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation, resulting in energy waves having substantially higher transport efficiency along the longitudinal orientation, and spatial localization along the transverse orientation. In some embodiments where the relay is constructed of multicore fiber, the energy waves propagating within each relay element may travel in the longitudinal orientation determined by the alignment of fibers in this orientation.

In other embodiments, each of the plurality of relay elements (e.g. 8304, 8306, 8308, 8310, 8312) is configured to transport energy along the longitudinal orientation, and wherein the energy waves propagating through the plurality of relay elements have higher transport efficiency in the longitudinal orientation than in the transverse orientation due to the randomized refractive index variability such that the energy is localized in the transverse orientation. In some embodiments, the energy waves propagating between the relay elements may travel substantially parallel to the longitudinal orientation due to the substantially higher transport efficiency in the longitudinal orientation than in the transverse orientation. In other embodiments, randomized refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation results in energy waves having substantially higher transport efficiency along the longitudinal orientation, and spatial localization along the transverse orientation.

FIG. 82 illustrates an arrangement 8400 of multiple optical taper relay modules coupled together with perpendicular energy source side geometries 8404, 8406, 8408, 8410, and 8412, and a convex energy source surface 8402 that is radial about a center axis, in accordance with one embodiment of the present disclosure. FIG. 82 illustrates a modification of the configuration shown in FIG. 81, with perpendicular energy source side geometries and a convex output energy surface that is radial about a center axis.

FIG. 83 illustrates an arrangement 8500 of multiple optical relay modules coupled together with perpendicular output energy surface 8502 and a convex energy source side surface 8504 radial about a center axis, in accordance with another embodiment of the present disclosure.

In some embodiments, by configuring the source side of the array of energy relays in a cylindrically curved shape about a center radius, and having a flat energy output surface, the input energy source acceptance angle and the output energy source emission angles may be decoupled, and it may be possible to better align each energy source module to the energy relay acceptance cone, which may itself be limited due to constraints on parameters such as energy taper relay magnification, NA, and other factors.

FIG. 84 illustrates an arrangement 8600 of multiple energy relay modules with each energy output surface independently configured such that the viewable output rays of light, in accordance with one embodiment of the present disclosure FIG. 84 illustrates the configuration similar to that of FIG. 83, but with each energy relay output surface independently configured such that the viewable output rays of light are emitted from the combined output energy surface with a more uniform angle with respect to the optical axis (or less depending on the exact geometries employed).

FIG. 85 illustrates an arrangement 8700 of multiple optical relay modules where both the emissive energy source side and the energy relay output surface are configured with various geometries producing explicit control over the input and output rays of light, in accordance with one embodiment of the present disclosure. To this end, FIG. 85 illustrates a configuration with five modules where both the emissive energy source side and the relay output surface are configured with curved geometries allowing greater control over the input and output rays of light.

FIG. 86 illustrates an arrangement 8800 of multiple optical relay modules whose individual output energy surfaces have been ground to form a seamless concave cylindrical energy source surface which surrounds the viewer, with the source ends of the relays flat and each bonded to an energy source.

In the embodiment shown in FIG. 86, and similarly in the embodiments shown in FIGS. 81, 82, 83, 84 and 85, a system may include a plurality of energy relays arranged across first and second directions, where in each of the relays, energy is transported between first and second surfaces which defines the longitudinal orientation, the first and second surfaces of each of the relays extends generally along a transverse orientation defined by the first and second directions, where the longitudinal orientation is substantially normal to the transverse orientation. Also in this embodiment, energy waves propagating through the plurality of relays have higher transport efficiency in the longitudinal orientation than in the transverse orientation due to high refractive index variability in the transverse orientation coupled with minimal refractive index variation in the longitudinal orientation. In some embodiments where each relay is constructed of multi core fiber, the energy waves propagating within each relay element may travel in the longitudinal orientation determined by the alignment of fibers in this orientation.

In one embodiment, similar to that discussed above, the first and second surfaces of each of the plurality of relay elements, in general, can curve along the transverse orientation and the plurality of relay elements can be integrally formed across the first and second directions. The plurality of relays can be assembled across the first and second directions, arranged in a matrix having at least a 2×2 configuration, and include glass, optical fiber, optical film, plastic, polymer, or mixtures thereof. In some embodiments, a system of a plurality of relays may be arranged across the first direction or the second direction to form a single tiled surface along the first direction or the second direction, respectively. Like above, the plurality of relay elements can be arranged in other matrices including without limitation a 3×3 configuration, a 4×4 configuration, a 3×10 configuration, and other configurations as can be appreciated by one skilled in the art. In other embodiments, seams between the single tiled surface may be imperceptible at a viewing distance of twice a minimum dimension of the single tiled surface.

For a mosaic of energy relays, the following embodiments may be included: both the first and second surfaces may be planar, one of the first and second surfaces may be planar and the other non-planar, or both the first and second surfaces may be non-planar. In some embodiments, both the first and second surfaces may be concave, one of the first and second surfaces may be concave and the other convex, or both the first and second surfaces may be convex. In other embodiments, at least one of the first and second surfaces may be planar, non-planar, concave or convex. Surfaces that are planar may be perpendicular to the longitudinal direction of energy transport, or non-perpendicular to this optical axis.

In some embodiments, the plurality of relays can cause spatial magnification or spatial de-magnification of energy sources, including but not limited to electromagnetic waves, light waves, acoustical waves, among other types of energy waves. In other embodiments, the plurality of relays may also include a plurality of energy relays (e.g., such as faceplates for energy source), with the plurality of energy relays having different widths, lengths, among other dimensions. In some embodiments, the plurality of energy relays may also include loose coherent optical relays or fibers.

Limitations of Anderson Localization Materials and Introduction of Ordered Energy Localization

While the Anderson localization principle was introduced in the 1950s, it wasn't until recent technological breakthroughs in materials and processes allowed the principle to be explored practically in optical transport. Transverse Anderson localization is the propagation of a wave transported through a transversely disordered but longitudinally invariant material without diffusion of the wave in the transverse plane.

Transverse Anderson localization has been observed through experimentation in which a fiber optic face plate is fabricated through drawing millions of individual strands of fiber with different refractive index (RI) that were mixed randomly and fused together When an input beam is scanned across one of the surfaces of the face plate, the output beam on the opposite surface follows the transverse position of the input beam. Since Anderson localization exhibits in disordered mediums an absence of diffusion of waves, some of the fundamental physics are different when compared to optical fiber relays. This implies that the Anderson localization phenomena in the random mixture of optical fibers with varying RI arises less by total internal reflection than by the randomization between multiple-scattering paths where wave interference can completely limit the propagation in the transverse orientation while continuing in the longitudinal path Further to this concept, it is introduced herein that a non-random pattern of material wave propagation properties may be used in place of a randomized distribution in the transverse plane of an energy transport device. Such a non-random distribution may induce what is referred to herein as Ordered Energy Localization in a transverse plane of the device. This Ordered Energy Localization reduces the occurrence of localized grouping of similar material properties, which can arise due to the nature of random distributions, but which act to degrade the overall efficacy of energy transport through the device.

In an embodiment, it may be possible for Ordered Energy Localization materials to transport light with a contrast as high as, or better than, the highest quality commercially available multimode glass image fibers, as measured by an optical modulation transfer function (MTF). With multimode and multicore optical fibers, the relayed images are intrinsically pixelated due to the properties of total internal reflection of the discrete array of cores, where the loss of image transfer in regions between cores will reduce MTF and increase blurring. The resulting imagery produced with multicore optical fiber tends to have a residual fixed noise fiber pattern, as illustrated in FIG. 5A. By contrast, the same relayed image through an example material sample that exhibits Ordered Energy Localization, which is similar to that of the Transverse Anderson Localization principle, where the noise pattern appears much more like a grain structure than a fixed fiber pattern

Another advantage to optical relays that exhibit the Ordered Energy localization phenomena is that it they can be fabricated from a polymer material, resulting in reduced cost and weight. A similar optical-grade material, generally made of glass or other similar materials, may cost more than a hundred times the cost of the same dimension of material generated with polymers. Further, the weight of the polymer relay optics can be 10-100 times less. For the avoidance of doubt, any material that exhibits the Anderson localization property, or the Ordered Energy Localization property as described herein, may be included in this disclosure, even if it does not meet the above cost and weight suggestions. As one skilled in the art will understand that the above suggestion is a single embodiment that lends itself to significant commercial viabilities that similar glass products exclude. Of additional benefit is that for Ordered Energy Localization to work, optical fiber cladding may not be needed, which for traditional multicore fiber optics is required to prevent the scatter of light between fibers, but simultaneously blocks a portion of the rays of light and thus reduces transmission by at least the core-to-clad ratio (e.g. a core-to-clad ratio of 70:30 will transmit at best 70% of received illumination) In certain embodiments, relaying energy through all or most of the materials of a relay may improve the efficiency of relaying energy through said material, since the need for extra energy controlling materials may be reduced or eliminated.

Another benefit is the ability to produce many smaller parts that can be bonded or fused without seams as the polymer material is composed of repeating units, and the merger of any two pieces is nearly the same as generating the component as a singular piece depending on the process to merge the two or more pieces together For large scale applications, this is a significant benefit for the ability to manufacture without massive infrastructure or tooling costs, and it provides the ability to generate single pieces of material that would otherwise be impossible with other methods. Traditional plastic optical fibers have some of these benefits, but due to the cladding generally still involve a seam line of some distances.

The present disclosure includes engineered structure exhibiting the Ordered Energy Localization phenomena and the method of manufacturing same. The engineered structure of the present disclosure may be used to construct relays of electromagnetic energy, acoustic energy, or other types of energy using building blocks that may include one or more component engineered structures (“CES”). The term CES refers to a building block component with specific engineered properties (“EP”) that may include, but are not limited to, material type, size, shape, refractive index, center-of-mass, charge, weight, absorption, and magnetic moment, among other properties. The size scale of the CES may be on the order of wavelength of the energy wave being relayed, and can vary across the milli-scale, the micro-scale, or the nano-scale. The other EP's are also highly dependent on the wavelength of the energy wave.

Within the scope of the present disclosure, a particular arrangement of multiple CES may form a non-random pattern, which may be repeated in the transverse direction across a relay to effectively induce Ordered Energy Localization. A single instance of such a non-random pattern of CES is referred to herein as a module. A module may comprise two or more CES. A grouping of two or more modules within a relay is referred to herein as a structure.

Ordered Energy Localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, energy waves, among others. The one or more component engineered structures may form an energy wave relay that exhibits Ordered Energy Localization each have a size that is on the order of the corresponding wavelength. Another parameter for the building blocks is the speed of the energy wave in the materials used for those building blocks, which includes refractive index for electromagnetic waves, and acoustic impedance for acoustic waves. For example, the building block sizes and refractive indices can vary to accommodate any frequency in the electromagnetic spectrum, from X-rays to radio waves, or to accommodate acoustic waves ranging from ultra-low frequencies just above 0 Hz to ultrasonic frequencies of approximately 20 MHz

For this reason, discussions in this disclosure about optical relays can be generalized to not only the full electromagnetic spectrum, but to acoustical energy and other types of energy. For this reason, the use of the terms energy source, energy surface, and energy relay will be used in the present disclosure, even if an embodiment may be discussed with respect to one particular form of energy such as the visible electromagnetic spectrum. One of ordinary skill in the art would understand the principles of the present disclosure as discussed with respect to one form of energy would apply the same for embodiments implemented for other forms of energy.

For the avoidance of doubt, the material quantities, process, types, refractive index, and the like are merely exemplary and any optical material that exhibits the Ordered Energy Localization property is included herein. Further, any use of ordered materials and processes is included herein.

It should be noted that the principles of optical design noted in this disclosure apply generally to all forms of energy relays, and the design implementations chosen for specific products, markets, form factors, mounting, etc may or may not need to address these geometries but for the purposes of simplicity, any approach disclosed is inclusive of all potential energy relay materials.

In one embodiment, for the relay of visible electromagnetic energy, the transverse size of the CES should be on the order of 1 micron. The materials used for the CES can be any optical material that exhibits the optical qualities desired to include, but not limited to, glass, plastic, resin, air pockets, and the like The index of refraction of the materials used are higher than 1, and if two CES types are chosen, the difference in refractive index becomes a key design parameter. The aspect ratio of the material may be chosen to be elongated, in order to assist wave propagation in a longitudinal direction.

In embodiments, energy from other energy domains may be relayed using one or more CES. For example, acoustic energy or haptic energy, which may be mechanical vibrational forms of energy, may be relayed. Appropriate CES may be chosen based on transport efficiency in these alternate energy domains. For example, air may be selected as a CES material type in relaying acoustic or haptic energy. In embodiments, empty space or a vacuum may be selected as a CES in order to relay certain forms of electromagnetic energy. Furthermore, two different CES may share a common material type, but may differ in another engineered property, such as shape.

The formation of a CES may be completed as a destructive process that takes formed materials and cuts the pieces into a desired shaped formation or any other method known in the art, or additive, where the CES may be grown, printed, formed, melted, or produced in any other method known in the art. Additive and destructive processes may be combined for further control over fabrication. These CES are constructed to a specified structure size and shape.

In one embodiment, for electromagnetic energy relays, it may be possible to use optical grade bonding agents, epoxies, or other known optical materials that may start as a liquid and form an optical grade solid structure through various means including but not limited to LTV, heat, time, among other processing parameters. In another embodiment, the bonding agent is not cured or is made of index matching oils for flexible applications. Bonding agent may be applied to solid structures and non-curing oils or optical liquids. These materials may exhibit certain refractive index (RI) properties. The bonding agent needs to match the RI of either CES material type 1 or CES material type 2. In one embodiment, the RI of this optical bonding agent is 1.59, the same as PS (polystyrene). In a second embodiment, the RI of this optical bonding agent is 1.49, the same as PMMA (poly methyl methcacrylate). In another embodiment, the RI of this optical bonding agent is 1.64, the same as a thermoplastic polyester (TP) material.

In one embodiment, for energy waves, the bonding agent may be mixed into a blend of CES material type I and CES material type 2 in order to effectively cancel out the RI of the material that the bonding agent RI matches. The bonding agent may be thoroughly intermixed, with enough time given to achieve escape of air voids, desired distributions of materials, and development of viscous properties. Additional constant agitation may be implemented to ensure the appropriate mixture of the materials to counteract any separation that may occur due to various densities of materials or other material properties.

It may be required to perform this process in a vacuum or in a chamber to evacuate any air bubbles that may form. An additional methodology may be to introduce vibration during the curing process.

An alternate method provides for three or more CES with additional form characteristics and EPs.

In one embodiment, for electromagnetic energy relays, an additional method provides for only a single CES to be used with only the bonding agent, where the RI of the CES and the bonding agent differ.

An additional method provides for any number of CESs and includes the intentional introduction of air bubbles.

In one embodiment, for electromagnetic energy relays, a method provides for multiple bonding agents with independent desired RIs, and a process to intermix the zero, one, or more CES's as they cure either separately or together to allow for the formation of a completely intermixed structure. Two or more separate curing methodologies may be leveraged to allow for the ability to cure and intermix at different intervals with different tooling and procedural methodologies. In one embodiment, a UV cure epoxy with a RI of 1.49 is intermixed with a heat cure second epoxy with a RI of 1.59 where constant agitation of the materials is provisioned with alternating heat and UV treatments with only sufficient duration to begin to see the formation of solid structures from within the larger mixture, but not long enough for any large particles to form, until such time that no agitation can be continued once the curing process has nearly completed, whereupon the curing processes are implemented simultaneously to completely bond the materials together. In a second embodiment, CES with a RI of 1.49 are added. In a third embodiment, CES with both a RI of 1.49 and 1.5′9 both added.

In another embodiment, for electromagnetic energy relays, glass and plastic materials are intermixed based upon their respective RI properties.

In an additional embodiment, the cured mixture is formed in a mold and after curing is cut and polished In another embodiment, the materials leveraged will re-liquefy with heat and are cured in a first shape and then pulled into a second shape to include, but not limited to, tapers or bends.

It should be appreciated that there exist a number of well-known conventional methods used to weld polymeric materials together. Many of these techniques are described in ISO 472 (“Plastics-Vocabulary”, International Organization for Standardization, Switzerland 1999) which is herein incorporated by reference in its entirety, and which describes processes for uniting softened surfaces of material including thermal, mechanical (e.g. vibration welding, ultrasonic welding, etc.), electromagnetic, and chemical (solvent) welding methods

FIG. 7A illustrates a cutaway view of a flexible relay 70 exhibiting the Transverse Anderson Localization approach using CES material type 1 (72) and CES material type 2 (74) with intermixing oil or liquid 76 and with the possible use of end cap relays 79 to relay the energy waves from a first surface 77 to a second surface 77 on either end of the relay within a flexible tubing enclosure 78 in accordance with one embodiment of the present disclosure The CES material type 1 (72) and CES material type 2 (74) both have the engineered property of being elongated—in this embodiment, the shape is elliptical, but any other elongated or engineered shape such as cylindrical or stranded is also possible. The elongated shape allows for channels of minimum engineered property variation 75.

For an embodiment for visible electromagnetic energy relays, relay 70 may have the bonding agent replaced with a refractive index matching oil 76 with a refractive index that matches CES material type 2 (74) and placed into the flexible tubing enclosure 78 to maintain flexibility of the mixture of CES material type 1 and CES material 2, and the end caps 79 would be solid optical relays to ensure that an image can be relayed from one surface of an end cap to the other. The elongated shape of the CES materials allows channels of minimum refractive index variation 75.

Multiple instances of relay 70 can be interlaced into a single surface in order to form a relay combiner in solid or flexible form.

In one embodiment, for visible electromagnetic energy relays, several instances of relay 70 may each be connected on one end to a display device showing only one of many specific tiles of an image, with the other end of the optical relay placed in a regular mosaic, arranged in such a way to display the full image with no noticeable seams. Due to the properties of the CES materials, it is additionally possible to fuse the multiple optical relays within the mosaic together

FIG. 7B illustrates a cutaway view of a rigid implementation 750 of a CES Transverse Anderson Localization energy relay. CES material type 1 (72) and CES material type 2 (74) are intermixed with bonding agent 753 which matches the index of refraction of material 2 (74). It is possible to use optional relay end caps 79 to relay the energy wave from the first surface 77 to a second surface 77 within the enclosure 754 The CES material type 1 (72) and CES material type 2 (74) both have the engineered property of being elongated—in this embodiment, the shape is elliptical, but any other elongated or engineered shape such as cylindrical or stranded is also possible. Also shown in FIG. 7B is a path of minimum engineered property variation 75 along the longitudinal direction 751, which assists the energy wave propagation in this direction 751 from one end cap surface 77 to the other end cap surface 77.

The initial configuration and alignment of the CESs can be done with mechanical placement, or by exploiting the EP of the materials, including but not limited to: electric charge, which when applied to a colloid of CESs in a liquid can result in colloidal crystal formation; magnetic moments which can help order CESs containing trace amounts of ferromagnetic materials, or relative weight of the CESs used, which with gravity helps to create layers within the bonding liquid prior to curing.

In one embodiment, for electromagnetic energy relays, the implementation depicted in FIG. 7B may have the bonding agent 753 matching the index of refraction of CES material type 2 (74), the optional end caps 79 may be solid optical relays to ensure that an image can be relayed from one surface of an end cap to the other, and the EP with minimal longitudinal variation may be refractive index, creating channels 75 which would assist the propagation of localized electromagnetic waves.

In an embodiment for visible electromagnetic energy relays, FIG. 8 illustrates a cutaway view in the transverse plane the inclusion of a DEMA (dimensional extra mural absorption) CES, 80, along with CES material types 74, 82 in the longitudinal direction of one exemplary material at a given percentage of the overall mixture of the material, which controls stray light, in accordance with one embodiment of the present disclosure for visible electromagnetic energy relays.

The additional CES materials that do not transmit light are added to the mixture(s) to absorb random stray light, similar to EMA in traditional optical fiber technologies, except that the distribution of the absorbing materials may be random in all three dimensions, as opposed to being invariant in the longitudinal dimension. Herein this material is called DEMA, 80. Leveraging this approach in the third dimension provides far more control than previous methods of implementation. Using DEMA, the stray light control is much more fully randomized than any other implementation, including those that include a stranded EMA that ultimately reduces overall light transmission by the fraction of the area of the surface of all the optical relay components it occupies. In contrast, DEMA is intermixed throughout the relay material, absorbing stray light without the same reduction of light transmission. The DEMA can be provided in any ratio of the overall mixture. In one embodiment, the DEMA is 1% of the overall mixture of the material. In a second embodiment, the DEMA is 10% of the overall mixture of the material.

In an additional embodiment, the two or more materials are treated with heat and/or pressure to perform the bonding process and this may or may not be completed with a mold or other similar forming process known in the art. This may or may not be applied within a vacuum or a vibration stage or the like to eliminate air bubbles during the melt process. For example, CES with material type polystyrene (PS) and polymethylmethacrylate (PMMA) may be intermixed and then placed into an appropriate mold that is placed into a uniform heat distribution environment capable of reaching the melting point of both materials and cycled to and from the respective temperature without causing damage/fractures due to exceeding the maximum heat elevation or declination per hour as dictated by the material properties

For processes that require intermixing materials with additional liquid bonding agents, in consideration of the variable specific densities of each material, a process of constant rotation at a rate that prevents separation of the materials may be required.

Differentiating Anderson and Ordered Energy Relay Materials

FIG. 9 illustrates a cutaway view in the transverse plane of a portion 900 of a pre-fused energy relay comprising a randomized distribution of particles comprising two component materials, component engineered structure (“CES”) 902 and CES 904. In an embodiment, particles comprising either CES 902 or CES 904 may possess different material properties, such as different refractive indices, and may induce an Anderson Localization effect in energy transported therethrough, localizing energy in the transverse plane of the material. In an embodiment, particles comprising either CES 902 or CES 904 may extend into and out of the plane of the illustration in a longitudinal direction, thereby allowing energy propagation along the longitudinal direction with decreased scattering effects compared to traditional optical fiber energy relays due to the localization of energy in the transverse plane of the material.

FIG. 10 illustrates a cutaway view in the transverse plane of module 1000 of a pre-fused energy relay comprising a non-random pattern of particles, each particle comprising one of three component materials, CES 1002, CES 1004, or CES 1006. Particles comprising one of CES's 1002, 1004, or 1006 may possess different material properties, such as different refractive indices, which may induce an energy localization effect in the transverse plane of the module. The pattern of particles comprising one of CES's 1002, 1004, or 1006 may be contained within a module boundary 1008, which defines the particular pattern that particles comprising one of CES's 1002, 1004, or 1006 are arranged in. Similar to FIG. 9, particles comprising one of CES's 1002, 1004, or 1006 may extend in a longitudinal direction into and out of the plane of the illustration to allow energy propagation along the longitudinal direction with decreased scattering effects compared to traditional optical fiber energy relays due to the localization of energy in the transverse plane of the material.

Particles comprising one of CES's 902 or 904 from FIG. 9 and particles comprising one of CES's 1002, 1004, or 1006 from FIG. 10 may be long, thin rods of respective material which extend in a longitudinal direction normal to the plane of the illustration and are arranged in the particular patterns shown in FIG. 9 and FIG. 10 respectively. Although small gaps may exist between individual particles of CES due to the circular cross-sectional shape of the particles shown in FIG. 9 and FIG. 10, these gaps would effectively be eliminated upon fusing, as the CES materials would gain some fluidity during the fusing process and “melt” together to fill in any gaps. While the cross-sectional shapes illustrated in FIG. 9 and FIG. 10 are circular, this should not be considered limiting of the scope of this disclosure, and one skilled in the art should recognize that any shape or geometry of pre-fused material may be utilized in accordance with the principles disclosed herein. For example, in an embodiment, the individual particles of CES have a hexagonal rather than circular cross section, which may allow for smaller gaps between particles prior to fusing.

FIG. 11 illustrates a cutaway view in the transverse plane of a portion 1100 of a pre fused energy relay comprising a random distribution of particles comprising component materials CES 1102 and CES 1104. The portion 1100 may have a plurality of sub-portions, such as sub-portions 1106 and 1108 each comprising a randomized distribution of particles comprising CES 1102 and 1104. The random distribution of particles comprising CES 1102 and CES 1104 may, after fusing of the relay, induce a Transverse Anderson Localization effect in energy relayed in a longitudinal direction extending out of the plane of the illustration through portion 1100.

FIG. 13 illustrates a cutaway view in the transverse plane of a portion 1300 of a fused energy relay comprising a random distribution of particles comprising component materials CES 1302 and CES 1304. Portion 1300 may represent a possible fused form of portion 1100 from FIG. 11 In the context of the present disclosure, when adjacent particles of similar CES aggregate together upon fusing, this is referred to as an aggregated particle (“AP”). An example of an AP of CES 1302 can be seen at 1308, which may represent the fused form of several unfused CES 1302 particles (shown in FIG. 11). As illustrated in FIG. 13, the boundaries between each continuous particle of similar CES, as well as the boundaries between modules with similar CES border particles, are eliminated upon fusing, while new boundaries are formed between AP's of different CES.

According to the Anderson Localization principle, a randomized distribution of materials with different energy wave propagation properties distributed in the transverse direction of a material will localize energy within that direction, inhibiting energy scattering and reducing interference which may degrade the transport efficiency of the material. In the context of transporting electromagnetic energy, for example, through increasing the amount of variance in refractive index in the transverse direction by randomly distributing materials with differing refractive indices, it becomes possible to localize the electromagnetic energy in the transverse direction.

However, as discussed previously, due to the nature of randomized distributions, there exists the possibility that undesirable arrangements of materials may inadvertently form, which may limit the realization of energy localization effects within the material. For example, AP 1306 of FIG. 13 could potentially form after fusing the randomized distribution of particles shown in the corresponding location in FIG. 11. When designing a material for transporting electromagnetic energy, for example, a design consideration is the transverse size of pre-fused particles of CES. In order to prevent energy from scattering in the transverse direction, one may select a particle size such that upon fusing, the resultant average AP size is substantially on the order of the wavelength of the electromagnetic energy the material is intended to transport However, while the average AP size can be designed for, one skilled in the art would recognize that a random distribution of particles will result in a variety of unpredictable sizes of AP, some being smaller than the intended wavelength and some being larger than the intended wavelength.

In FIG. 13, AP 1306 extends across the entire length of portion 1300 and represents an AP of a size much larger than average. This may imply that the size of AP 1306 is also much larger than the wavelength of energy that portion 1300 is intended to transport in the longitudinal direction. Consequently, energy propagation through AP 1306 in the longitudinal direction may experience scattering effects in the transverse plane, reducing the Anderson Localization effect and resulting in interference patterns within energy propagating through AP 1306 and a reduction in the overall energy transport efficiency of portion 1300.

It should be understood that, according to the principles disclosed herein and due to the nature of randomized distributions, a sub-portion within portion 1100, such as sub-portion 1108 for example, may be of arbitrary significance, since there is no defined distribution pattern. However, it should be apparent to one skilled in the art that in a given randomized distribution, there exists the possibility that one may identify distinct sub-portions that comprise the same or substantially similar patterns of distribution. This occurrence may not significantly inhibit the overall induced Transverse Anderson Localization effect, and the random patterns described herein should not be seen as limited to exclude such cases.

The non-random, Ordered Energy Localization pattern design considerations disclosed herein represent an alternative to a randomized distribution of component materials, allowing energy relay materials to exhibit energy localization effects in the transverse direction while avoiding the potentially limiting deviant cases inherent to randomized distributions.

It should be noted that across different fields and throughout many disciplines, the concept of “randomness,” and indeed the notions of what is and is not random are not always clear. There are several important points to consider in the context of the present disclosure when discussing random and non-random patterns, arrangements, distributions, et cetera, which are discussed below. However, it should be appreciated that the disclosures herein are by no means the only way to conceptualize and/or systematize the concepts of randomness or non-randomness. Many alternate and equally valid conceptualizations exist, and the scope of the present disclosure should not be seen as limited to exclude any approach contemplated by one skilled in the art in the present context.

Complete spatial randomness (“CSR”), which is well-known in the art and is described in Smith, T. E., (2016) Notebook on Spatial Data Analysis [online] (http://www.seas.upenn.edu/˜ese502/#notebook), which is herein incorporated by reference, is a concept used to describe a distribution of points within a space (in this case, within a 2D plane) which are located in a completely random fashion. There are two common characteristics used to describe CSR: The spatial Laplace principle, and the assumption of statistical independence.

The spatial Laplace principle, which is an application of the more general Laplace principle to the domain of spatial probability, essentially states that, unless there is information to indicate otherwise, the chance of a particular event, which may be thought of as the chance of a point being located in a particular location, is equally as likely for each location within a space. That is to say, each location within a region has an equal likelihood of containing a point, and therefore, the probability of finding a point is the same across each location within the region. A further implication of this is that the probability of finding a point within a particular sub-region is proportional to the ratio of the area of that sub-region to the area of the entire reference region.

A second characteristic of CSR is the assumption of spatial independence. This principle assumes that the locations of other data points within a region have no influence or effect on the probability of finding a data point at a particular location. In other words, the data points are assumed to be independent of one another, and the state of the “surrounding areas”, so to speak, do not affect the probability of finding a data point at a location within a reference region.

The concept of CSR is useful as a contrasting example of a non-random pattern of materials, such as some embodiments of CES materials described herein. An Anderson material is described elsewhere in this disclosure as being a random distribution of energy propagation materials in a transverse plane of an energy relay. Keeping in mind the CSR characteristics described above, it is possible to apply these concepts to some of the embodiments of the Anderson materials described herein in order to determine whether the “randomness” of those Anderson material distributions complies with CSR. Assuming embodiments of an energy relay comprising first and second materials, since a CES of either the first or second material may occupy roughly the same area in the transverse plane of the embodiments (meaning they are roughly the same size in the transverse dimension), and further since the first and second CES may be assumed to be provided in equal amounts in the embodiments, we can assume that for any particular location along the transverse plane of the energy relay embodiments, there is an equally likely chance of there being either a first CES or a second CES, in accordance with spatial Laplace principle as applied in this context. Alternatively, if the relay materials are provided in differing amounts in other energy relay embodiments, or possess a differing transverse size from one another, we would likewise expect that the probability of finding either material be in proportion to the ratio of materials provided or to their relative sizes, in keeping with the spatial Laplace principle.

Next, because both the first and second materials of Anderson energy relay embodiments are arranged in a random manner (either by thorough mechanical mixing, or other means), and further evidenced by the fact that the “arrangement” of the materials may occur simultaneously and arise spontaneously as they are randomized, we can assert that the identities of neighboring CES materials will have substantially no effect on the identity of a particular CES material, and vice versa, for these embodiments. That is, the identities of CES materials within these embodiments are independent of one another. Therefore, the Anderson material embodiments described herein may be said to satisfy the described CSR characteristics. Of course, as discussed above, the nature of external factors and “real-world” confounding, factors may affect the compliance of embodiments of Anderson energy relay materials with strict CSR definitions, but one of ordinary skill in the art would appreciate that these Anderson material embodiments substantially fall within reasonable tolerance of such definitions.

By contrast, an analysis of some of the Ordered Energy Localization relay material embodiments as disclosed herein highlights particular departures from their counterpart Anderson material embodiments (and from CSR). Unlike an Anderson material, a CES material identity within an Ordered Energy Localization relay embodiment may be highly correlated with the identities of its neighbors. The very pattern of the arrangement of CES materials within certain Ordered Energy Localization relay embodiments is designed to, among other things, influence how similar materials are arranged spatially relative to one another in order to control the effective size of the APs formed by such materials upon fusing In other words, one of the goals of some embodiments which arrange materials in an Ordered Energy Localization distribution is to affect the ultimate cross-sectional area (or size), in the transverse dimension, of any region comprising a single material (an AP). This may limit the effects of transverse energy scattering and interference within said regions as energy is relayed along a longitudinal direction. Therefore, some degree of specificity and/or selectivity is exercised when energy relay materials are first “arranged” in an Ordered Energy Localization distribution embodiment, which may disallow for a particular CES identity to be “independent” of the identity of other CES, particularly those materials immediately surrounding it. On the contrary, in certain embodiments materials are specifically chosen according to a non-random pattern, with the identity of any one particular CES being determined based on a continuation of the pattern and in knowing what portion of the pattern (and thus, what materials) are already arranged. It follows that these certain Ordered Energy Localization distribution energy relay embodiments cannot comply with CSR criteria. Thus, the pattern or arrangement of two or more CES or energy relay materials may be described in the present disclosure as “non-random” or “substantially non-random,” and one of ordinary skill in the art should appreciate that the general concept or characteristics of CSR as describe above may be considered, among other things, to distinguish non-random or substantially non-random pattern from random pattern For example, in an embodiment, materials that do not substantially comply with the general concept or characteristics of CSR as described, may be considered an Ordered Energy Localization material distribution. In this disclosure, the term ‘ordered’ may be recited to describe a distribution of component engineered structure materials for relays that transmits energy through the principle of Ordered Energy Localization. The term ‘ordered energy relay’, ‘ordered relay’, ‘ordered distribution’, ‘non-random pattern’, etc., describe an energy relay in which energy is transmitted at least partially through this same principle of Ordered Energy Localization described herein.

Of course, the CSR concept is provided herein as an example guideline to consider, and one of ordinary skill in the art may consider other principles known in the art to distinguish non-random patterns from random patterns. For example, it is to be appreciated that, like a human signature, a non-random pattern may be considered as a non-random signal that includes noise. Non-random patterns may be substantially the same even when they are not identical due to the inclusion of noise. A plethora of conventional techniques exist in the art of pattern recognition and comparison that may be used to separate noise and non-random signals and correlate the latter. By way of example, U.S. Pat. No. 7,016,516 to Rhoades, which is incorporated by reference herein, describes a method of identifying randomness (noise, smoothness, snowiness, etc.), and correlating non-random signals to determine whether signatures are authentic. Rhodes notes that computation of a signal's randomness is well understood by artisans in this field, and one example technique is to take the derivative of the signal at each sample point, square these values, and then sum over the entire signal. Rhodes further notes that a variety of other well-known techniques can alternatively be used. Conventional pattern recognition filters and algorithms may be used to identify the same non-random patterns. Examples are provided in U.S. Pat. Nos. 5,465,308 and 7,054,850, all of which are incorporated by reference herein. Other techniques of pattern recognition and comparison will not be repeated here, but it is to be appreciated that one of ordinary skill in the art would easily apply existing techniques to determine whether an energy relay comprises a plurality of repeating modules each comprising at least first and second materials being arranged in a substantially non-random pattern, are in fact comprising the same substantially non-random pattern

Furthermore, in view of the above-mentioned points regarding randomness and noise, it should be appreciated that an arrangement of materials into a substantially non-random pattern may, due to unintentional factors such as mechanical inaccuracy or manufacturing variability, suffer from a distortion of the intended pattern. An example of such a distortion is illustrated in FIG. 20B, where a boundary 2005 between two different materials is affected by the fusing process such that it has a unique shape not originally part of the non-random arrangement of materials illustrated in FIG. 20A. It would be apparent to one skilled in the art, however, that such distortions to a non-random pattern are largely unavoidable and are intrinsic to the nature of the mechanical arts, and that the non-random arrangement of materials shown in FIG. 20A is still substantially maintained in the fused embodiment shown in FIG. 20B, despite mechanical distortions to the boundaries of said materials. Thus, when considering an arrangement of materials, it is within the capabilities of one such skilled in the art to distinguish a distorted portion of a pattern from an undistorted portion, just as one would identify two signatures as belonging to the same person despite their unique differences.

FIG. 12A illustrates a cutaway view in the transverse plane of a portion 1200 of a pre fused energy relay comprising a non-random pattern (a distribution configured to relay energy via Ordered Energy Localization) of three component materials CES 1202, CES 1204, or CES 1206, which define multiple modules with similar orientations. Particles of these three CES materials are arranged in repeating modules, such as module 1208 and module 1210, which share substantially invariant distributions of said particles While portion 1200 contains six modules as illustrated in FIG. 12A, the number of modules in a given energy relay can be any number and may be chosen based on the desired design parameters. Additionally, the size of the modules, the number of particles per module, the size of the individual particles within a module, the distribution pattern of particles within a module, the number of different types of modules, and the inclusion of extra-modular or interstitial materials may all be design parameters to be given consideration and fall within the scope of the present disclosure.

Similarly, the number of different CES's included within each module need not be three as illustrated in FIG. 12A, but may preferably be any number suited to the desired design parameters. Furthermore, the different characteristic properties possessed by each CES may be variable in order to satisfy the desired design parameters, and differences should not be limited only to refractive index. For example, two different CES's may possess substantially the same refractive index, but may differ in their melting point temperatures

In order to minimize the scattering of energy transported through the portion 1200 of the energy relay illustrated in FIG. 12A, and to promote transverse energy localization, the non-random pattern of the modules that comprise portion 1200 may satisfy the Ordered Energy Localization distribution characteristics described above. In the context of the present disclosure, contiguous particles may be particles that are substantially adjacent to one another in the transverse plane. The particles may be illustrated to be touching one another, or there may be an empty space illustrated between the adjacent particles One skilled in the art will appreciate that small gaps between adjacent illustrated particles are either inadvertent artistic artifacts or are meant to illustrate the minute mechanical variations which can arise in real-world arrangement of materials. Furthermore, this disclosure also includes arrangements of CES particles in substantially non-random patterns, but contain exceptions due to manufacturing variations or intentional variation by design.

Ordered Energy Localization patterns of CES particles may allow for greater localization of energy, and reduce scattering of energy in a transverse direction through a relay material, and consequently allow for higher efficiency of energy transport through the material relative to other embodiments. FIG. 12B illustrates a cutaway view in the transverse plane of a portion 1250 of a pre-fused energy relay comprising a non-random pattern of particles of three component materials, CES 1202, CES 1204, and CES 1206, wherein the particles define multiple modules with varying orientations. Modules 1258 and 1260 of portion 1250 comprise a non-random pattern of materials similar to that of modules 1208 and 1210 of FIG. 12A However, the pattern of materials in module 1260 are rotated relative to that of module 1258. Several other modules of portion 1250 also exhibit a rotated pattern of distribution. It is important to note that despite this rotational arrangement, each module within portion 1250 possesses the Ordered Energy Localization distribution described above, since the actual pattern of particle distribution within each module remains the same regardless of how much rotation is imposed upon it.

FIG. 14 illustrates a cutaway view in the transverse plane of a portion 1400 of a fused energy relay comprising a non-random pattern of particles of three component materials, CES 1402, CES 1404, and CES 1406 Portion 1400 may represent a possible fused form of portion 1200 from FIG. 12A. By arranging CES particles in an Ordered Energy Localization distribution, the relay shown in FIG. 14 may realize more efficient transportation of energy in a longitudinal direction through the relay relative to the randomized distribution shown in FIG. 13. By selecting CES particles with a diameter roughly ½ of the wavelength of energy to be transported through the material and arranging them in a pre-fuse Ordered Energy Localization distribution shown in FIG. 12A, the size of the resultant AP's after fusing seen in FIG. 14 may have a transverse dimension between ½ and 2 times the wavelength of intended energy. By substantially limiting transverse AP dimensions to within this range, energy transported in a longitudinal direction through the material may allow for Ordered Energy Localization and reduce scattering and interference effects In an embodiment, a transverse dimension of AP's in a relay material may preferably be between ¼ and 8 times the wavelength of energy intended to be transported in a longitudinal direction through the APs.

As seen in FIG. 14, and in contrast with FIG. 13, there is notable consistency of size across all APs, which may result from exerting control over how pre-fused CES particles are arranged. Specifically, controlling the pattern of particle arrangement may reduce or eliminate the formation of larger AP's with larger energy scattering, and interference patterns, representing, an improvement over randomized distributions of CES particles in energy relays.

FIG. 15 illustrates a cross-sectional view of a portion 1500 of an energy relay comprising a randomized distribution of two different CES materials, CES 1502 and CES 1504. Portion 1500 is designed to transport energy longitudinally along the vertical axis of the illustration, and comprises a number of AP's distributed along the horizontal axis of the illustration in a transverse direction. AP 1510 may represent an average AP size of all the AP's in portion 1500 As a result of randomizing the distribution of CES particles prior to fusing of portion 1500, the individual AP's that make up portion 1500 may substantially deviate from the average size shown by 1510. For example, AP 1508 is wider than AP 1510 in the transverse direction by a significant amount. Consequently, energy transported through AP's 1510 and 1508 in the longitudinal direction may experience noticeably different localization effects, as well as differing amounts of wave scattering and interference. As a result, upon reaching its relayed destination, any energy transported through portion 1500 may exhibit differing levels of coherence, or varying intensity across the transverse axis relative to its original state when entering portion 1500. Having energy emerge from a relay that is in a significantly different state than when it entered said relay may be undesirable for certain applications such as image light transport

Additionally, AP 1506 shown in FIG. 15 may be substantially smaller in the transverse direction than average-sized AP 1510. As a result, the transverse width of AP 1506 may be too small for energy of a certain desired energy wavelength domain to effectively propagate through, causing degradation of said energy and negatively affecting the performance of portion 1500 in relaying said energy.

FIG. 16 illustrates a cross-sectional view of a portion 1600 of an energy relay comprising a non-random pattern of three different CES materials, CES 1602, CES 1604, and CES 1606. Portion 1600 is designed to transport energy longitudinally along the vertical axis of the illustration, and comprises a number of AP's distributed along the horizontal axis of the illustration in a transverse direction. AP 1610, comprising CES 1604, and AP 1608, comprising CES 1602, may both have substantially the same size in the transverse direction. All other AP's within portion 1600 may also substantially share a similar AP size in the transverse direction. As a result, energy being transported longitudinally through portion 1600 may experience substantially uniform, localization effects across the transverse axis of portion 1600, and suffer reduced scattering and interference effects. By maintaining a consistent AP width in the transverse dimension, energy which enters portion 1600 will be relayed and affected equally regardless of where along the transverse direction it enters portion 1600. This may represent an improvement of energy transport over the randomized distribution demonstrated in FIG. 15 for certain applications such as image light transport

FIG. 17 illustrates a cross-sectional perspective view of a portion 1700 of an energy relay comprising a randomized distribution of aggregated particles comprising component materials CES 1702 and 1704. In FIG. 17, input energy 1706 is provided for transport through portion 1700 in a longitudinal direction (y-axis) through the relay, corresponding with the vertical direction in the illustration as indicated by the arrows representing energy 1706, The energy 1706 is accepted into portion 1700 at side 1710 and emerges from portion 1700 at side 1712 as energy 1708 Energy 1708 is illustrated as having varying sizes and pattern of arrow's which are intended to illustrate that energy 1708 has undergone non-uniform transformation as it was transported through portion 1700, and different portions of energy 1708 differ from initial input energy 1706 by varying amounts in magnitude and localization in the transverse directions (x axis) perpendicular to the longitudinal energy direction 1706.

As illustrated in FIG. 17, there may exist an AP, such as AP 1714, that possesses a transverse size that is too small, or otherwise unsuited, for a desired energy wavelength to effectively propagate from side 1710 through to side 1712. Similarly, an AP such as AP 1716 may exist that is too large, or otherwise unsuited, for a desired energy wavelength to effectively propagate from side 1710 through to side 1712. The combined effect of this variation in energy propagation properties across portion 1700, which may be a result of the randomized distribution of CES particles used to faun portion 1700, may limit the efficacy and usefulness of portion 1700 as an energy relay material.

FIG. 18 illustrates a cross-sectional perspective view of a portion 1800 of an energy relay comprising a non-random pattern of aggregated particles of three component materials, CES 1802, CES 1804, and CBS 1806. In FIG. 18, input energy 1808 is provided for transport through portion 1800 in a longitudinal direction through the relay, corresponding with the vertical direction in the illustration as indicated by the arrows representing energy 1808 The energy 1808 is accepted into portion 1800 at side 1812 and is relayed to and emerges from side 1814 as energy 1810. As illustrated in FIG. 18, output energy 1810 may have substantially uniform properties across the transverse direction of portion 1800. Furthermore, input energy 1808 and output energy 1810 may share substantially invariant properties, such as wavelength, intensity, resolution, or any other wave propagation properties. This may be due to the uniform size and distribution of AP's along the transverse direction of portion 1800, allowing energy at each point along the transverse direction to propagate through portion 1800 in a commonly affected manner, which may help limit any variance across emergent energy 1810, and between input, energy 1808 and emergent energy 1810.

Ordered Energy Relay Material Design Considerations

FIG. 19 illustrates a cutaway view in the transverse plane of a portion 1900 of a pre-fused energy relay comprising a non-random pattern of particles arranged in one of two module structures, module structure 1908, composed of CES 1902, CES 1904, and CES 1906, or module structure 1912, composed of CES 1910, CES 1914, and CES 1916 Including two different module structures in portion 1900, may further allow for control over the propagation of energy waves longitudinally through portion 1900. For example, CES 1910 may be an energy absorbing material, or otherwise act to inhibit the propagation of energy, referred to herein as an energy inhibiting material. In various embodiments, energy inhibiting materials may inhibit energy propagation via absorption, reflection, scattering, interference, or any other means known in the art. By including a material with these properties periodically throughout the non-random pattern of CES particles in portion 1900, the energy wave propagation properties of portion 1900 may be manipulated for a desired result, such as a refined numerical aperture.

In another embodiment, an energy relay may contain two different module structures optimized for the transport of two different energy sources. For example, in FIG. 19, the module structures 1912 may be optimized for the visible electromagnetic spectrum, with CES 1902, 1904, and 1906 having a size that is comparable with the wavelength of visible light, and having a range of refractive indices appropriate for the transmission of visible light, while the module structures 1908 may be optimized for the transport of ultrasonic waves, with CES 1910, CES 1914, and CES 1916 having a range of acoustic impedance values selected for the transmission of ultrasonic sound waves, and each with a size comparable with the wavelength of the sound waves being transmitted.

The specific non-random pattern shown in FIG. 19 is for exemplary purposes only, and one skilled in the art should recognize that there are many aspects of a non-random pattern one may preferably alter in order to yield a desired result while still falling within the scope of the present disclosure. For example, FIG. 19 illustrates two distinct module patterns 1912 and 1908. However, there may be non-random patterns with one, two, three, or more, distinct module patterns. Furthermore, the size of CES particles or modules may either be uniform or may vary between modules, as shown in FIG. 19. Modules may also exist with similar patterns of particle distribution but vary in size, for example. The various ratios of different modules in a relay material or the specific arrangement of modules within a relay material may also be adjusted. Additionally, a relay material may also include non-CES elements, such as intentionally included empty spaces or air bubbles or gaps which may impart some benefit to the material. Interstitial materials may also be included between modules, or between particles within a module. It should also be appreciated that manufacturing complexities may lead to defects wherein a non-random pattern may deviate from the intended non-random pattern, and one skilled on the art should appreciate that these deviations are inadvertent and should not be limiting of the scope of the present disclosure.

FIG. 20A illustrates a perspective view of a pre-fused module 2000 featuring an arrangement of particles comprising one of three different CES materials, CES 2002, CES 2004, or CES 2006 The particles comprising module 2000 are arranged in a non-random pattern with variable particle size. FIG. 20B illustrates a perspective view of module 2000 after it has been fused. As illustrated in FIG. 20A and FIG. 20B, the size of individual particles can be selected to be any preferable size. Also of note is the fact that when designing a module, consideration should be paid as to how a particular arrangement of CES particles will be affected by the fusing process. For example, although there is noticeable empty space surrounding CES particles comprising CES 2006 in the center of FIG. 20A, upon fusing the individual particles form an AP 2008 in FIG. 20B comprised of CES 2006 and the voided space is then filled with CES 2006 material. This allows for significant flexibility in designing non-random pattern relay materials as well as in the manufacturing process, and expands the number of possible designs.

FIG. 20C illustrates a cutaway view in the transverse plane of a portion 2010 of a pre-fused energy relay comprising a distribution of particles and a non-random pattern of additional structures 2012. FIG. 20D illustrates a cutaway view in the transverse plane of the fused portion 2010 comprising the particles and additional structures 2012. In an embodiment, the additional structures 2012 may be energy inhibiting structures. In traditional optical fibers using a core-clad configuration, an energy wave propagation material is surrounded by an energy inhibiting cladding in order to contain the energy within the propagation material. The addition of the cladding around the energy propagation material is an additional step which adds to the manufacturing complexity and design constraints in many cases. By incorporating inhibiting structures within the pre-fused distribution of energy wave propagation materials, the cost, complexity, and efficacy of the inhibiting structures may be greatly improved Furthermore, by selecting where the inhibiting structures are located within the energy relay material in the transverse direction, as well as the size of the inhibiting structures, it is possible to further reduce energy wave diffusion, scattering, and interference effects compared to conventional core-clad design schema.

FIG. 20E illustrates a perspective view of a module 2020 of a pre-fused energy relay comprising a non-random pattern of hexagonally shaped particles, each particle comprising one of CES 2022, CES 2024, or CES 2026. The boundaries between CES material region 2022, 2024, and 2026 are straight lines. FIG. 20F illustrates a perspective view of module 2020 after it has been fused, with the borders between CES material regions 2022, 2024, and 2026 that are no longer perfectly straight, but are substantially in the same location as the pre-fused boundaries. FIG. 20E and FIG. 20F demonstrate that the individual shape of particles which comprise an energy relay material can be designed and customized to any preferable shape or arrangement. Furthermore, by designing and arranging CES materials with a regular hexagonal shape, it becomes much easier to predict how the non-random pattern will appear once the fusing process is complete. Module 2020 after fusing in FIG. 20F is nearly identical to the pre-fused arrangement shown in FIG. 20E. In addition, there are a number of shapes and configurations for CES particles besides a regular hexagonal tiling which allow for this advantage, collectively referred to as convex uniform tidings, Convex uniform tidings and their potential application within the context of the present disclosure will be addressed in forthcoming sections herein.

Further to the embodiments demonstrated in the preceding paragraphs, FIG. 20G illustrates a perspective view of a module 2030 of a pre-fused energy relay comprising a non-random pattern of irregularly shaped CES regions. FIG. 20G demonstrates the concept that the individual size, shape, material, or any other property of a particle may be advantageously selected based on the particular design constraints preferably imposed. Analysis of FIG. 20G reveals that despite several particles having an irregular size or shape, a non-random pattern is still possible using module 2030. Thus, an energy relay material composed of modules resembling module 2030 may still realize Ordered Energy Localization despite having many irregular substituents, and may in fact represent an improvement over randomized distributions of materials for certain applications

FIG. 20H illustrates a perspective cross-sectional view of a portion 2040 of a pre-fused tube and pellet system for manufacturing an energy relay, and FIG. 20I illustrates a perspective cross-sectional view of portion 2040 after fusing. Rather than providing long, thin rods of CES material which are then arranged into a non-random pattern and fused together, it is possible to arrange a number of hollow bodies of CES material and fill those tubes with additional CES material, then fuse the entire tube and pellet system to yield an energy relay material,

In FIG. 20H, tube 2042 may comprise CES 2044 and may be arranged adjacent to tubes 2043 and 2045, where 2043 and 2045 may comprise a CES material different than CES 2044 Tube 2042 may then be filled with pellets 2046 of a material different than CES 2044, A filler material 2048 may then be placed in the voids or interstitial regions 2041 between tubes 2042, 2043, and 2045, which may be an additional CES material, an energy inhibiting material, or any other preferable material. The tube and pellet system shown in FIG. 20H may then be fused and produce the portion 2040 shown in FIG. 20I Upon fusing, all pellets 2046 within tube 2044 may form AP 2047, and filler material 2048 may flow to occupy interstitial regions 2041. By appropriately selecting the size of the tubes, the size of the pellets, the material types of each tube and pellet, and the material type of any interstitial materials, it becomes possible to use the tube and pellet system shown in FIG. 20H and FIG. 20I to produce energy relay materials exhibiting Ordered Energy Localization consistent with the present disclosure.

FIG. 20J illustrates a cutaway view in the transverse plane of a module 2050 of a pre-fused energy relay comprising a non-random pattern of particles comprising one of CES 2052, CES 2054, or CES 2056, CES 2056 may preferably be chosen as a material with energy inhibiting or energy absorbing properties and particles comprising CES 2056 may preferably be arranged to form micro-sized energy inhibiting structures which can be embedded within the non-random pattern of module 2050. Adding energy, inhibiting structures to the pattern of Ordered Energy Localization distribution within an energy relay module may provide an easier-to-manufacture method of controlling energy propagation properties through the material, such as controlling the numerical aperture of the energy relay. Furthermore, by leveraging Ordered Energy Localization principles to control factors such as numerical aperture, focal length, chief ray angle, etc., it may be possible to realize higher energy transport efficiency through Ordered Energy Localization inducing materials as well as to reduce the amount of inhibiting material.

FIG. 20K illustrates a cutaway view in the transverse plane of a module 2060 of a pre-fused energy relay comprising a non-random pattern of particles comprising one of CES 2052, CES 2054, or CES 2056, and a surrounding energy inhibiting material comprising CES 2058 Rather than placing inhibiting structures within a non-random pattern distribution as shown in FIG. 20J, it is also possible to surround a non-random patterned energy relay module with energy inhibiting material. This approach ensures that energy is contained and localized within the non-random pattern of module 2060, and ensures reduced diffusion of said energy outside the boundaries of the module 2060 by leveraging energy inhibiting CES 2058.

FIG. 21A illustrates a cross-sectional view in the transverse plane of a pre-fused energy relay 2100 comprising a flexible outer enclosure 2102, end caps 2104, and pellets of energy transport material arranged in a non-random pattern comprising one of CES 2106, CES 2108, or CES 2110. Relay 2100 is similar to the flexible energy relay shown in FIG. 7A, but rather than having a randomized distribution of energy transport materials, features a non-random pattern of energy transport materials. Importantly, the composition at any point in the transverse direction, such as plane 2114, should maintain a non-random pattern of CES materials to effectively induce an Ordered Energy Localization effect. Additionally, along the longitudinal direction, such as path 2116, there should be constant CES material to promote propagation of energy waves in the longitudinal direction.

A system for forming flexible relay 2100 may include providing flexible enclosure 2102 and adding CES materials into flexible enclosure 2102 in a non-random pattern. Then, end caps 2104 are positioned in place at the ends of enclosure 2102 to seal the CES materials within the flexible relay 2100. Finally, the relay 2100 may be fused to secure the CES materials in their designated locations within the non-random pattern.

There may exist voids between CES materials within the flexible relay 2100, such as void 2112. Void 2112 may preferably be left empty, whereupon fusing, CES material will flow into and occupy void 2112, or an interstitial material may be introduced to relay 2100 in order to occupy empty space between CES materials. The interstitial material may also have energy wave propagation properties or energy wave inhibition properties as desired.

FIG. 21B illustrates a cross-sectional view of a fused version of flexible relay 2100. Importantly, CES materials 2106, 2108, and 2110 are continuous in the longitudinal direction, which may promote more efficient transport of energy through relay 2100.

FIG. 21C illustrates a cross sectional view of flexible relay 2100 in a non-fused and non-flexed state, and FIG. 21D illustrates a cross-sectional view of flexible relay 2100 in a fused and non-flexed state. Of note is that flexible enclosure 2100 may be in a flexed or non-flexed state either before or after fusing, and the underlying design criteria and principles of energy transport being levered in a flexible energy relay are still in effect

Methods for Macro-Scale Production of Ordered Energy Relay Microstructures

FIG. 22A illustrates a cutaway view in the transverse plane of a system for forming non-random pattern of energy relay materials (for Ordered Energy Localization relay of energy). In FIG. 22A, a module 2200 of an energy relay is shown comprising a non-random pattern of particles comprising one of CES 2202, CES 2204, or CES 2206. As illustrated in FIG. 22A, module 2200 may have a certain initial size, which is a result of the size of CES particles which define module 2200, as well as the particular pattern that the particles are arranged in. By applying heat and pulling module 2200 along a longitudinal direction, as previously discussed in the present disclosure, it becomes possible to reduce the size of module 2200 down to a smaller diameter while maintaining the specific non-random pattern of CES materials which define module 2200. The resulting reduced-sized module 2208 shown in FIG. 22B may have substantially the same non-random pattern of materials as module 2200, but may be substantially smaller in a transverse direction, effectively changing the energy wavelength domain of energy which may be effectively transported through module 2208 in a longitudinal direction. The general distribution of CES materials has been preserved in the reduced-sized module 2208, although the fusing process will cause some local variation or deformation in the shape of CES material regions. For example, the single rod of CES 2202 has become CES material 2203, the CES 2204 and its two contiguous neighbors have become fused region 2205 with roughly the same shape, and the single rod of CES 2206 has deformed to a roughly hexagonal-shaped CES 2207.

FIG. 22B illustrates a cutaway view in the transverse plane of a system for forming non-random pattern of energy relay materials and represents a fused version of the module 2200 shown in FIG. 22A. The principles described in reference to FIG. 22A are also applicable to FIG. 22B. By fusing a material before pulling it to a reduced-size module 2208, there may be less variation imposed as a result of the pulling process, and the reduced-size energy relay may possess a more predictable material distribution. In one embodiment, the fusing process may include heating up the relay material to a temperature that is less than the glass transition temperature of one or more of the component engineered structures that comprise the relay. In a different embodiment, the relay material is heated to a temperature that is close to the glass transition temperature of one or more of the component engineered structures, or the average glass transition temperature of the component engineered structures that comprise the relay. In an embodiment, the fusing process may include using a chemical reaction to fuse the relay materials together, optionally with a catalyst. In an embodiment, the fusing process may include placing the arrangement of component engineered structures into a constrained space, and then applying heat. The constrained space may be provided by a fixture similar to the ones shown in FIG. 26A-26E which are configured to define a constrained space 2606. In an embodiment, the fusing process may include placing the arrangement of component engineered structures into a constrained space, applying a compressive force to the energy relay materials, and then applying heat. This is particularly useful if the component engineered structures are polymers with biaxial tension, where the compressive force prevents the materials from warping or shrinking as they are fused together or annealed. In this way, the fusing step also involves relaxing the material, and may be referred to as a fusing and relaxing step. In an embodiment, the fusing and relaxing process may include a sequence of steps with process parameters, where each step includes one of: using a chemical reaction to fuse the energy relay materials, optionally with a varying level of catalyst; constraining the arrangement and applying a compressive force with a desired force level; applying heat to a desired temperature level, which may be close to the glass transition temperature of one or more of the component engineered structures of the relay, and applying cooling to a desired temperature. The fused and relaxed material may then be released from the constrained space after fusing, has completed.

FIG. 23 illustrates a. continuation of the process 2300 shown in FIG. 22B. Multiple reduced-sized modules 2208 of an energy relay may be arranged into the grouping as shown in portion 2301. By applying heat and pulling module 2301 along a longitudinal direction, as previously discussed and shown in FIGS. 22A and 22B, it becomes possible to taper the size of composite module 2301 down to smaller microstructure module 2302, while maintaining the specific non-random pattern of CES materials which define module 2301. This process can be repeated again using module 2302 to yield the even small microstructure module 2304. Any desirable number of iterations of this process can be performed in order to achieve a desired microstructure size. Since module 2301 is itself composed of shrunken modules 2208, the original distribution of CES materials which define 2208 has been preserved, but made even smaller in the transverse dimension, in such a way that 2304 also shares the same non-random pattern as portions 2301, as illustrated by a blow-up 2306 of a sub-portion of portion 2304. Outline 2308 represents the original size of portion 2301 compared to the reduced-size portion 2304. This process can then be repeated any number of times to yield non-random pattern energy relays of a desired transverse size having started from larger materials. For example, multiple modules 2304 may be arranged in a similar grouping of 2301, and the process repeated. This system makes it possible to form micro-level distribution patterns without having to manipulate individual CES materials on the micro scale, meaning that manufacturing of energy relays can remain in the macro-scale. This may simplify the overall manufacturing process, reducing manufacturing complexity and expense. This size-reduction process can also provide more precise control over the actual transverse dimension and patterning of the CES materials, which enables one to custom tailor a relay to a specific desired energy wavelength domain

FIG. 24 illustrates a block-diagram of the heating and pulling process of forming energy relay materials. In step 2402, CES materials are first arranged in a desired non-random pattern. In step 2404, the materials may further be arranged into a constrained space. In step 2406, the energy relay materials are fused together in the constrained space, where fusing/relaxing may be a sequence of steps, where each step may include any of: applying compressive stress to the arrangement of energy relay materials, applying heat, applying cooling, or using a chemical reaction, possibly with a catalyst. In step 2408, the non-random materials are removed from the constrained space. In the next step 2410, the energy relay materials are then heated to the appropriate temperature, which in some embodiments may be the glass transition temperature of one or more of the non-random CES materials. In step 2412, the materials are then pulled into reduced-size microstructure rods, as shown above in FIGS. 22B and 23. The reduced size microstructure rods produced in step 2412 are then arranged into a desired non-random pattern again, similar to the bundle 2301 in FIG. 23, in step 2414. The non-random arrangement of microstructure rods may again return to step 2404 to be constrained, fused/relaxed, heated, pulled, and arranged in order to form a second order reduced size microstructure rod, similar to the microstructure 2304 shown in FIG. 23. If the second-order microstructure rods, produced in step 2414 need to undergo further heating and pulling to adjust their energy transport domain, step 2404 may be returned to using the second-order microstructure rods, and the ensuing steps may be repeated a desired number of times to produce energy relay materials of the desired size and configuration to relay energy in the desired energy domain, containing n^(th) order microstructure rods. At the final step of the process 2416, the final arrangement of microstructure rods is fused/relaxed to form an energy relay.

FIG. 25 illustrates an embodiment for forming energy relays with a reduced transverse dimension, and represents a visualization of some of the steps of the process described in FIG. 24. First, a material with a non-random pattern of CES's is provided, such as module 2502, which is constrained, fused/relaxed, and released It is then heated and pulled to form reduced dimension module 2504. The discontinuity seen between the original module 2502 and the reduced dimension module 2504 is an artistic representation of the above-described process whereby the transverse dimension of the original module 2502 is reduced to that of module 2504, though they are in fact the same material. Once a sufficient number of reduced dimension modules 2504 have been produced, they may be re-assembled in a new non-random pattern shown at 2508. This new non-random pattern 2508 comprises a plurality of reduced-size modules 2504, which may then undergo a similar process of being constrained, fused/relaxed, released, heated and pulled to produce the reduced dimension module shown at 2506. The discontinuity seen between the non-random pattern 2508 and the reduced dimension module 2506 is an artistic representation of the above-described process whereby the transverse dimension of the original distribution 2508 is reduced to that of module 2506, though they are in fact the same material. This process may be iterated as many times as desired in order to produce an energy relay of a preferable size, containing a preferable density of energy relay material channels for relaying energy.

Fixturing Methods Addressing Biaxial Stress for Forming Energy Relays

FIG. 26A illustrates a perspective view of system 2600 for fusing energy relay materials by fixing the pre-fused relay materials 2606 in a fixture comprising two pieces 2602 and 2604. Materials 2606 may be arranged in a non-random pattern prior to placing within fixtures 2602 and 2604, after which they are held by the fixtures in the non-random pattern In embodiments, the non-random pattern of materials 2606 may be formed within the interior space between fixtures 2602 and 2604 after they have been assembled together. In an embodiment, relaxation of materials 2606 may occur before, during, or after fusing the relay materials 2606.

FIG. 26B illustrates an embodiment in which fixtures 2602 and 2604 are assembled and contain energy relay materials as part of fusing the energy relay materials. The assembled fixtures 2602 and 2604 containing a non-random pattern of materials 2606 may then be heated by applying heat 2614 for a suitable amount of time at a suitable temperature. In an embodiment, the amount of time and temperable for applying may be determined based on the relay materials' material properties, including the change in structural stress due the addition or removal of heat. In an embodiment, relaxing of materials 2606 may be a pre-fusing process whereby the materials are held at a temperature or within a range of temperatures for an extended period of time in order to release structural stresses, including, for example, those from the annealed relaxation of the stress in biaxial materials, and help the materials form more effective bonds during the fusing process. If energy relay materials are not relaxed before fusing, the material may “relax” after the fusing process has occurred and suffer a deformation or delamination with adjacent materials or the CES material distribution may otherwise be compromised by shifting in an undesired way. The relaxation method is intended to prevent this by preparing the non-random pattern of relay materials for the fusing process so that the non-random pattern may be maintained to a greater degree after fusing. Additionally, relaxing materials may make for a more effective draw or pull of the material during the process illustrated in FIG. 24 Once the relaxation process is complete, the materials 2606 may remain in fixtures 2602 and 2604 as the system is heated to the fusing temperature by adjusting heat 2614, and materials 2606 are fused together, or the materials may be removed from the fixtures 2602 and 2604 prior to fusing.

FIG. 26C illustrates the materials shown at 2606 in FIG. 26B having been fused together, to form the fused ordered energy relay material 2608. In the embodiment shown, the relay materials are kept inside the fixtures 2604 and 2602 during the relay fusing process, and then the resulting fused relay 2608 as illustrated in FIG. 28 is removed from the fixture. In embodiments, the energy relay materials may be removed from fixtures 2602 and 2604 prior to fusing

Additionally, in an embodiment the fixtures 2602 and 2604 may be configured to apply a compressive force 2610 on the energy relay materials. The compressive force 2610 may be directed along the transverse plane of the energy relay materials in order to provide resistance to expansion or deformation along the transverse plane as internal stresses are relaxed in the material. This compressive force 2610 may be adjustable, such that the amount of compressive force may be increased or decreased as desired, in combination with temperature changes applied to the energy relay materials. In embodiments, the compressive force 2610 may further be variable along the longitudinal orientation, such that different portions of the energy relay material may experience different amounts of compressive force simultaneously This compressive force 2610 may be applied with bolts 2612 that clamp fixture components 2602 and 2604 together, where the bolts 2612 are distributed along the length of the relay.

FIG. 26D illustrates a perspective view of a fixture 2601 for fusing energy relay materials with movable strips on each interior surface of the fixture in order to apply a radially inward compressive force In the embodiment illustrated in FIG. 26D, the interior sides of fixture components 2602 and 2604 may contain movable strips 2621 extending the length of the fixture 2601, that may apply force 2610 towards the constrained space 2606 defined by the fixture 2601, oriented towards the center of relay materials, such as materials 2608 from FIG. 26C, which may be constrained within the fixture 2601. Each strip 2621 may be composed primarily of a structurally stiff material such as aluminum, steel, carbon fiber, or a composite material, and may be tightened via multiple bolts 2623 that are threaded through each side of the fixture components 2602 and 2604. Each strip 2621 may have a pliable surface 2622, such as rubber attachment, mounted to the interior side of the strip 2621, where an interior surface of the pliable surface 2622 defines the constrained space 2606. The pliable surface 2622 may assist in distributing the force 2610 applied to each strip 2621 evenly to the energy relay materials constrained in the constrained space 2606. In this embodiment, clamping bolts 2612 are used to keep the components 2602 and 2604 of the fixture 2601 attached together as force 2610 is applied to the strips 2621 via tightening of the bolts 2623

FIG. 26E illustrates a cross-sectional view of the fixture 2601 along a transverse plane of the fixture 2601. Bolts 2623 may extend through the fixture from an interior to an exterior side, and may be threaded to secure bolts 2623 in place and allow adjustment of their positions. As bolts 2623 are adjusted, the force 2610 applied to the movable strips 2621 is increased or decreased, thereby allowing adjustment of the compressive force 2610 applied to the constrained space 2606, and any energy relay materials which may be constrained therein, such as materials 2608 from FIG. 26C. Fixture 2601 allows for a variation in compressive force both longitudinally from one end of the fixture to another, but also transversely, as individual bolts 2623 may be adjusted independently of one another. Furthermore, bolts 2623 may be adjusted at different times, allowing adjustment of compressive force 2610 temporally as well.

FIG. 27 illustrates a block diagram of the process of forming an energy relay. In step 2702 the CES energy relay materials are arranged in a desired non-random pattern. Then, in step 2704, the energy relay materials are secured in a fixture. In step 2706, the fixture containing the energy relay materials arranged in the non-random pattern is subjected to one or more of processing steps, where each processing step is one of: applying a compressive force to the energy relay materials; applying heating to the energy relay materials; cooling the relay materials, or using a chemical reaction to fuse the relay materials, which may involve use of a catalyst. In one embodiment, the energy relay materials are heated to an appropriate temperature or range of temperatures for a desired amount of time to sufficiently relax and fuse the materials, and the compressive forces on the relay material may be adjusted at different temperatures to remove air gaps and ensure the component engineered structure materials fuse together. Then in step 2708, the relaxed, fused energy relay materials are removed from the fixture.

FIG. 28 illustrates a perspective view of a fused block of ordered energy relay materials 2606 after having been relaxed, fused, and released from fixtures 2602 and 2604 of FIG. 26B. The materials 2608 is now a continuous block of energy relay material no longer having discernable individual particles, but rather a continuous arrangement of aggregated particles (AP) of CES material. However, the non-random material distribution is still preserved and will induce Ordered Energy Localization along the transverse direction of the material. Block 2608 may now undergo additional heating and pulling in order to reduce the transverse dimensions of block 2606, as shown in FIGS. 22B, 23, and 25, with reduced risk of material deformation. FIG. 24 illustrates a block diagram of a combined overall process for manufacturing micro-scale ordered energy relay materials.

In an embodiment, some amount of material deformation may exist. Deformation may occur during any of the processes described herein, including during said heating, pulling, fixturing, or other disclosed steps or processes One skilled in the art should appreciate that while care may be taken to avoid unwanted material deformation, the materials may still experience unintended deformations. For example, comparing the embodiments illustrated in FIGS. 20E and 20F, FIGS. 20A and 20B, or FIGS. 26B and 26C, one can see a slight deformation of the borders of the individual CES materials. While this may introduce some amount of uniqueness to each particular CES, it should be understood that minute deformations of CES materials that occur during processing should not be given consideration when identifying a substantially non-random pattern as disclosed herein, and do not represent a departure from said non-random pattern.

Due to the flexibility of the material chosen to be used for relaying energy according to the present disclosure, one may preferably design an energy relay material using flexible or partially flexible materials capable of bending or deforming without compromising their structure or energy wave propagation properties. With traditional glass optical fibers, the glass rods remain largely inflexible throughout the production process, making manufacturing difficult and expensive. By leveraging more robust materials with greater flexibility, cheaper and more efficient manufacturing avenues may be used.

Combining Transverse Dimensional Reduction and Fixture Forming Methods

FIGS. 29A and 29B illustrate a system 3000 for efficiently manufacturing ordered microstructure energy relay materials using a rotational drum. In system 3000, energy relay materials 3004 arranged in a non-random pattern may be provided and held in place by fixture 3002, where 3002 may be similar in form to that of fixture 2600. At 3006, a furnace may be provided, or another type of forming apparatus designed to produce the required form, size, or ordering of the relay materials 3004 At 3006, the materials 3004 may be pulled or drawn into a reduced size, flexible thread of energy relay material shown at 3008. Importantly, while the transverse dimension of materials 3008 is less than that of materials 3004, the non-random arrangement of energy relay materials present in materials 3004 is substantially maintained in flexible materials 3008. The flexible material 3008 may be conveyed by a motorized control system which may be used to maintain an appropriate speed for processing materials to a consistent size, shape, order, design, or other parameter. Alignment hardware 3010 is provided, which may be configured to rel ay the materials within the necessary tolerance of their flexibility, to avoid breakage and maintain the appropriate alignment of the material along the manufacturing process 3000. A positioner may be provided at 3012, which provides automated or semi-automated geometric alignment of the flexible material 3008 to the appropriate spacing and positioning relative to drum 3014. The positioner may have a positioning head (not shown) with a specific shape to match the flexible material 3008 and provide increased accuracy when aligning the material 3008 with the drum 3014. Drum 3014 may be a computer-controlled or motor-controlled drum that rotates at a speed commensurate with the draw speed of the flexible material 3008. The drum 3014 may include a mechanical or laser/optical measurement system (not shown) to automatically adjust the speed of the drum 3014's rotation or other motion to ensure consistent and accurate ordering is maintained. The drum 3014 may comprise a number of ordering molds 3016 along the circumference, as shown in FIG. 29A, or may comprise a singular, circumferential mold 3016 as shown in FIG. 29B. Ordering molds 3016 collect the material 3008 as it is drawn from relay material 3004, with the material having a predetermined non-random ordering that is maintained by the speed of the drum and the motion of positioner 3012. The ordering molds 3016 may be any parent shape (e.g. round, hex, etc.) as desired for fusing, and are generally configured as half or a partial section of a material fixture, similar to fixture 3002, where 3002 may be similar in form to that illustrated in system 2600. In an embodiment illustrated in FIG. 29B, drum 3014 may comprise a single fixture extending around the circumference of the drum. As drum 3014 rotates, flexible material 3008 is positioned at the appropriate location within the ordering molds 3016, eventually filling the molds 3016, and forming a second arrangement of materials 3005. Once molds 3016 are filled with second arrangements 3005 comprising a non-random arrangement of flexible material 3008, the material 3005 may be severed at interstitial sites 3018 to separate the filled molds 3016. In the embodiment shown at FIG. 29B, the continuous spool of second arrangement material 3005 may be severed at desired locations in order to produce segments of a desired length, whether to be a final product, or to be recycled through the illustrated process Prior to cutting, the molds 3016 may be fused, sealed, compressed, or otherwise secured such that the ordering of the materials 3005 within the molds 3016 is maintained. This process may be iteratively repeated by using a filled mold 3016 as the preform fixture 3002, wherein the second arrangement of materials 3005 may be used in place of material 3004 at the beginning of the process shown in FIGS. 29A and 29B until a desired energy relay material has been obtained.

Embodiments of the second arrangement of materials 3005 comprises a plurality of segments of flexible materials 3008, which themselves are reduced transverse dimensional versions of the energy relay materials 3004 which were arranged in a non-random pattern. Thus, said embodiments of second arrangement of materials 3005 comprise a plurality of miniaturized, non-random arrangements of energy relay materials, and are therefore also considered non randomly arranged, Ordered Energy Localization inducing materials.

Once a second arrangement of materials 3005 is obtained, it may be recycled through the illustrated process, replacing energy relay materials 3004 The result of the recycling of second arrangement 3005 would yield a corresponding third arrangement (not illustrated), which itself would comprise a plurality of miniaturized (reduced transverse dimension) segments of second arrangement 3005. This process can be repeated any number of times in order to yield a material such that the original, non-random arrangement of energy relay materials (originally present in materials 3004) now possesses a transverse dimension configured to localize energy of a desired domain (such as a desired range of wavelengths in the case of light energy).

In an embodiment, the fixture 3002 securing the energy relay materials 3004, may be further configured to apply a compressive force on the materials 3004 in order to force them through the forming apparatus 3006 to promote reforming of the materials 3004 into the reduced transverse dimension materials 3008. In another embodiment, the fixture 3002 may instead be configured to have an external force applied to it, such as by an electric motor or other similar source of force, in order to ultimately force the relay materials 3004 through forming apparatus 3006.

Optimized Ordered Geometries for Ordered Energy Localization

Several different geometries for CES particles and material pre-forms have been illustrated thus far. One aspect of the present disclosure is that any arrangement or geometry of materials may be leveraged, so long as they comprise a non-random pattern as previously discussed. However, the pre-fused relay material geometry may have a significant impact on the efficiency of the localization and energy propagation properties of the materials. In an embodiment, certain geometries, known as convex uniform filings, may provide advantageous distributions of relay materials by arranging the materials in efficient configurations.

In general, a tiling or tessellation is an arrangement of geometric shapes where there is substantially no overlap between the shapes and there are no gaps between the shapes. A tessellation can arranged on a 2-dimensional surface using planar shapes, or in 3-dimensions using volumetric structures. Furthermore, there exist subtypes within the domain of tiling. A regular tiling, for example, is a tessellation wherein each tile is the same shape. There are many non-regular tilings comprising a set of two or more shapes configured to tessellate with one another according. There are also non-periodic tilings which have no repeating pattern, as well as aperiodic tilings which use a set of repeating tile shapes that cannot form a repeating pattern, such as a Penrose tiling. All subtypes of tiling fall within the scope of the present disclosure. The shapes of the tiles, in two-dimensional embodiments, may be polygonal, convex, concave, curved, irregular, etc. Additionally, it should be apparent to one of ordinary skill in the art that while the definition of a tiling precludes there being gaps or space between tiles, there are real-world circumstances that sometimes cause deviation from strict definition, and that the existence of minor gaps or spaces between particular tiles should not be seen as a departure from a particular tiling or tessellation pattern.

For the relays of certain energy domains, there may also exist a desirability to use air as a CES energy transport material, which may be incorporated into a tiling pattern as disclosed herein. Therefore, the existence of air or empty space between other types of CES tiles may be an intentional gap by design, and may be a continuation of the tessellation in particular embodiments.

A tessellation may also be performed in higher dimensions, such as 3-dimensional space. The same principles disclosed above apply to these tessellations.

The Laves filings, for example, have vertices at the centers of the regular polygons, and edges connecting centers of regular polygons that share an edge. The tiles of the Laves tilings are called planigons including 3 regular tiles (triangle, square and pentagon) and 8 irregular ones. Each vertex has edges evenly spaced around it. Three dimensional analogues of the planigons are called stereohedrons

All reflectional forms can be made by Wythoff constructions, represented by Wythoff symbols, or Coxeter-Dynkin diagrams, each operating upon one of three Schwarz triangles (4,4,2), (6,3,2), or (3,3,3), with symmetry represented by Coxeter groups, [4,4], [6,3], or [3[3]]. Only one uniform tiling can't be constructed by a Wythoff process, but can be made by an elongation of the triangular tiling An orthogonal mirror construction [∞,2,∞] also exists, seen as two sets of parallel mirrors making a rectangular fundamental domain. If the domain is square, this symmetry can be doubled by a diagonal mirror into the [4,4] family. We disclose the geometries that may be leveraged.

A percolation model is to take a regular lattice, like a square lattice, and make it into a random network by randomly “occupying” sites (vertices) or bonds (edges) with a statistically independent probability p. At a threshold p_(c), large structures and long-range connectivity first appears, and this is called the percolation threshold. Depending on the method for obtaining the random network, one distinguishes between the site percolation threshold and the bond percolation threshold More general systems have several probabilities p₁, p₂, etc., and the transition is characterized by a surface or manifold. One can also consider continuum systems, such as overlapping disks and spheres placed randomly, or the negative space

When the occupation of a site or bond is completely random, this is the so-called Bernoulli percolation. For a continuum system, random occupancy corresponds to the points being placed by a Poisson process. Further variations involve correlated percolation, such as percolation structures related to Ising and Potts models of ferromagnets, in which the bonds are put down by the Fortuin- Kasteleyn method. In bootstrap or k-sat percolation, sites and/or bonds are first occupied and then successively culled from a system if a site does not have at least k neighbors. Another important model of percolation, in a different universality class altogether, is directed percolation, where connectivity along a bond depends upon the direction of the flow.

Simply, duality in two dimensions implies that all fully triangulated lattices (e.g., the triangular, union jack, cross dual, martini dual and asanoha or 3-12 dual, and the Delaunay triangulation) all have site thresholds of ½, and self-dual lattices (square, martini-B) have bond thresholds of ½.

Leveraging tiled structures may have the result of altering the respective holographic pixel aspect ratio, while providing variation in field of view spatially and/or volumetrically.

Reduction in moire or repeating patterns may also provide increased effective resolution and simultaneously provides higher potential levels of accuracy (increase in depth of field) by virtue of the various convergence locations that may be addressed Increased efficiency of resolution may also be achieved by packing more effective resolution in potential dimensions that are more ideal for applications by not necessarily leveraging a repeating single orientation or pattern.

Several embodiments of patterns that represent the spatial distribution of relay materials in the plane transverse to the longitudinal direction of energy wave propagation, which spatially localize the energy waves in this transverse plane via the principle of Ordered Energy Localization, are illustrated in FIG. 30-FIG. 58G.

FIG. 30 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials having one of two shapes. The specific tiling shown in FIG. 30 is a square tiling (or quadrille tiling).

FIG. 31 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes The specific tiling shown in FIG. 31 is a truncated square tiling (or truncated quadrille).

FIG. 32 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes. The specific tiling shown in FIG. 32 is a modified version of a truncated square tiling.

FIG. 33 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 33 is a Tetrakis square tiling (kisquadrille).

FIG. 34 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials having one of two shapes. The specific tiling shown in FIG. 34 is a snub square tiling (snub quadrille)

FIG. 35 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 35 is a Cairo pentagonal tiling (4-fold pentille).

FIG. 36 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 36 is a hexagonal tiling (hextille).

FIG. 37 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials all sharing the same shape The specific tiling shown in FIG. 37 is a triangular tiling (deltille).

FIG. 38 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials having one of two shapes. The specific tiling shown in FIG. 38 is a trihexagonal tiling (hexacleltille).

FIG. 39 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 39 is a rhombille tiling (rhombille).

FIG. 40 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes. The specific tiling shown in FIG. 40 is a truncated hexagonal tiling (truncated hextille).

FIG. 41 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape The specific tiling shown in FIG. 41 is a triakis triangular tiling (kisdeltille).

FIG. 42 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of three shapes. The specific tiling shown in FIG. 42 is a rhombitrihexagonal tiling (rhombihexadeltille).

FIG. 43 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 43 is a deltoidal trihexagonal tiling (tetrille).

FIG. 44 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of three shapes. The specific tiling shown in FIG. 44 is a truncated trihexagonal tiling (truncated hexadeltille)

FIG. 45 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 45 is a kisrhombille tiling (kisrhombille).

FIG. 46 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes. The specific tiling shown in FIG. 46 is a snub trihexagonal tiling (snub hextille).

FIG. 47 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 47 is a floret pentagonal tiling (6-fold pentille).

FIG. 48 illustrates a cutaway view in the transverse plane of a convex uniform tiling of four different energy relay materials having one of two shapes. The specific tiling shown in FIG. 48 is an elongated triangular tiling (isosnub quadrille).

FIG. 49 illustrates a cutaway view in the transverse plane of a convex uniform tiling of two different energy relay materials all sharing the same shape. The specific tiling shown in FIG. 49 is a prismatic pentagonal tiling (iso(4-)pentille).

FIG. 50 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes. The specific tiling shown in FIG. 50 is a trihexagonal tiling.

FIG. 51 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of three shapes The specific tiling shown in FIG. 51 is a rhombitrihexagonal tiling.

FIG. 52 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of three shapes. The specific tiling shown in FIG. 52 is a truncated trihexagonal tiling.

FIG. 53 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes. The specific tiling shown in FIG. 53 is a snub hexagonal tiling.

FIG. 54 illustrates a cutaway view in the transverse plane of a non-convex uniform tiling of four different energy relay materials having one of two shapes.

FIG. 55 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials all sharing the same shape.

FIG. 56 illustrates a cutaway view in the transverse plane of a convex uniform tiling of three different energy relay materials having one of two shapes

FIG. 57 illustrates a cutaway view in the transverse plane of a convex uniform tiling of four different energy relay materials having one of two shapes.

FIGS. 58A-58G illustrate cutaway views in the transverse plane of a several additional convex uniform tilings of one, two, three or more different energy relay materials.

The patterns illustrated in FIGS. 30-58G may be leveraged to represent not only distributions of relay materials, but also may be applied to design energy waveguide arrays that project energy from specific locations on an energy relay surface to specific angles in space. For example, in the visible electromagnetic energy spectrum, the above patterns may represent varied aperture sizes, aperture orientations, and different effective focal lengths across a lens array to yield an ordering to the projection patterns that is unachievable through typical regularly-spaced micro-lens array patterns.

The tilings shown in FIGS. 30-58G are merely exemplary, and the scope of the present disclosure should not be limited to these illustrated tilings.

Higher-Dimensional Ordered Energy Localization

In addition to the geometries previously disclosed herein, which have all been cross-sectional and planar, there are now introduced additional multi-dimensional non-random patterns of energy relay materials. By arranging certain three-dimensional shapes comprised of various CES materials into the disclosed non-random patterns, it becomes possible to form a non-random energy relay using three-dimensional non-random patterns capable of exhibiting Ordered Energy Localization effects.

The three-dimensional shapes may be configured such that they are able to be tessellated in three-dimensions This allows for an efficient way to arrange CES materials in three-dimensions substantially without gaps between the materials. Furthermore, the three-dimensional shapes may all be similar, or may be selected from a set of shapes configured to tessellate three-dimensionally, embodiments of which are disclosed below. FIG. 59 illustrates a perspective view of a deconstructed assembly of ordered pyramids 6000 comprising three different CES materials 6004, 6006, and 6008. In FIG. 59, there are three square pyramids of CES 6004, two square pyramids of CES 6006, and one square pyramid of CES 6008. By combining the six square pyramids shown in FIG. 59, a solid cube of energy relay material may be formed. After being assembled, the cube of material may exhibit localization of energy in both transverse and longitudinal orientations. An energy propagation pathway 6002 may be seen moving through the three square pyramidal shapes of similar CES material 6004, which are shaded grey in FIG. 59. The three-dimensional arrangement of different CES materials may be configured to localize energy transportation in a transverse plane of the energy relay, and may be further configured to promote propagation of energy in a longitudinal plane of the energy relay, consistent with the Ordered Energy Localization principles disclosed herein.

FIG. 60 illustrates a perspective view of a partially deconstructed configuration of the assembly of ordered pyramids 6000 comprising CES materials 6004, 6006, and 6008. By isolating only pyramids of CES 6004, the pathway 6002 can be seen propagating along only materials of CES 6004, creating an energy propagation pathway in the longitudinal direction which may exhibit energy localization effects. Once the ordered pyramids 6000 are assembled into the volumetric structure 6300 shown in FIG. 62, the pathway 6002 will be substantially linear and extend through only materials of similar CES 6004. The remaining three pyramids of CES's 6006 and 6008 would then be moved into position, interlocking with the CES 6004 pyramids.

The solid assembly may be formed through any methods comprising heat, fusing, chemical methods, time, adhesives, molding, or any methods of forming relay materials previously disclosed herein. The longitudinal localization with the Ordered Energy Localization properties may be maintained if the non-random distribution criteria are appropriately applied in consideration of not only a cross-section, but also dimensionally, as illustrated in FIG. 60.

FIG. 61 illustrates a perspective view of an expanded assembly of ordered pyramids 6001 comprising three different CES materials 6004, 6006, and 6008. The original six square pyramids of material forming assembly 6000 from FIG. 59 and FIG. 60 can be seen at the center of the expanded assembly 6001. Additional pyramids 6010 comprising one of the original three CBS materials can also be seen abutting the central cube, expanding the particular CES material type outwardly from the assembly 6000. The plurality of square pyramidal materials forming assembly 6000, in addition to the additional square pyramidal materials 6010, act as substructures which, when combined into expanded assembly 6001, form a composite shape comprising a rhombic dodecahedron. A longitudinal cross-section of the expanded assembly 6001 can be seen at 6012, and a transverse cross-section can be seen at 6014.

To allow for self-alignment of multiple volumetric structures, various forms of interlocking and non-regular dimensional geometries are disclosed. In FIG. 61, a rhombic dodecahedron is illustrated with the appropriate ordering accounted for to provide appropriate localization in any orientation, and accounts for the boundary conditions that will form from the interlocking of adjacent volumetric structures.

The fused (or otherwise processed) assemblies form a singular dimensional geometric shape that is designed such that all space is dimensionally filled. There still exists the possibility for non-perfect geometry where fusing or other processes (including liquid optical materials or other) may be applied to fill residual gaps. However, the ability to either form, or directly fabricate these geometric forms with the ordering considered provides the ability to directly or indirectly produce these manufactured ordered shapes that may be more easily produced without the necessity for multiple additional fabrication steps (e.g. pulling, fusing, material collection drums, etc) and may self- align with interlocking geometries and retain the appropriate non-random configuration regardless of individual rotation/placement of each volumetric structure.

Throughout the medium of the volumetric structure, Ordered Energy Localization is maintained for efficient energy propagation when tessellated with other volumetric structures.

FIG. 62 illustrates a perspective view of an assembled ordered volumetric structure 6300. A plurality of structure 6300 may be arranged in three-dimensional space to produce an energy relay with non-random patterning of materials in three-dimensions capable of inducing an energy localization effect in the longitudinal and transverse (not illustrated) directions, such as along propagation path 6302. The propagation path 6302 may be substantially linear through the volumetric structure 6300 In an embodiment, energy propagation along a substantially linear propagation path 6302 in a longitudinal direction through volumetric structure may experience higher transport efficiency in the longitudinal direction due to the localization effects described herein.

FIG. 63 illustrates a perspective view of a plurality of the ordered volumetric structures 6300 from FIG. 62 in geometric tessellation with boundary conditions accounted for to enable efficient localization of energy.

Due to the interlocking design of the rhombic dodecahedron, or any other desired dimensional configuration, the volumetric structures may align together to fill all residual space within a volume and appropriately account for Ordered Energy Localization. These structures may be formed together with vibration, pressure, vacuum, heat, liquid, gas, or any other process to interlock them together and form a material with as few gaps as possible. Further processing as defined in the previous sections (compression, heat, fusing, etc.) may be additionally applied, and these structures may be considered a dimensional preform to undergo all other disclosed inventions. Further, there may include multiple patterns, multiple dimensional interlocking (or non-interlacing) geometries, multiple sizes, patterns, etc for various energy propagation and localization design considerations It is also noted that the resultant interlocking structures may not be a solid, and may potentially be a liquid, or a flexible structure to enable the ordered structures to move for various applications.

Ordered Energy Localization volumetric structures used in the manufacture of an energy relay material may possess further properties that aid with the manufacturing process. For example, a non-random volumetric structure may feature a mechanism for orienting the structure in space. A structure may be weighted on one side, for example, or may have a magnetic moment and react to magnetic fields to orient itself in a certain direction in space. By carefully controlling, these properties, it may be possible for ordered volumetric structures to self-assemble or partially self-assemble into an energy relay material. In an embodiment, a plurality of ordered volumetric structures may each possess a particular electric dipole moment and exist in a common, uncompressed medium. When an electromagnetic field is applied to the plurality of structures, they may orient themselves such that they may be effectively compressed into an energy relay assembly. Other methods of orienting ordered volumetric structures besides weighting and electrical I magnetic polarization may exist, and may also include manual or computerized mechanical manipulation of the structures. Certain embodiments of CES volumetric structures may further be self-assembling, due to their particular engineered properties. For example, they may self-orient when introduced in bulk to one another, or a stimulus may be applied to cause an ordering of the volumetric structures.

FIG. 64 illustrates a perspective view of an assembly 6500 comprising additional ordered volumetric structures 6300, and demonstrates that they may be added in all dimensions to form larger and larger assemblies in order to achieve a desired size or configuration.

FIG. 65A illustrates a cross-sectional view in the transverse direction of the assembly 6500 of structures 6300 from FIG. 64. When designed with Ordered Energy Localization appropriately, for any given cross-section of the resultant materials after processing/forming, the same “rules” can apply as these geometries maintain higher order of similar material for localization in the longitudinal orientation and may exhibit further inhibiting of energy propagation in a transverse orientation, as shown by the dashed lines in FIG. 65A, A plurality of non-viable propagation paths 6602 is illustrated, demonstrating how the design of the ordered volumetric structures can inhibit transverse energy propagation through assembly 6500.

FIG. 65B illustrates a cross-sectional view in the longitudinal direction of an assembly 6500 of ordered volumetric structures of energy relay material. The dotted regions, such as region 6702, are locations that are attached in front or behind the cross section allowing for longitudinal propagation of energy. Ordering of the materials in FIG. 65B requires one of the dimensions to be ordered with the appropriate orientation (e.g. the axis cannot change), however, all other aspects of the design may rotate freely. The squiggly solid lines going through 6500 show possible energy propagation paths 6302 where the variation in the engineered property is minimized, promoting energy propagation. The propagation path 6302 may be substantially linear in a three-dimensional sense, but is illustrated as squiggly due to the way the cross-sectional view of FIG. 65B is presented.

FIG. 66A-C FIG. 67A-C, FIG. 68A-F, FIG. 69A-C, FIG. 70A-C, and FIG. 71 illustrates several variations and diagrams of the ordered volumetric structure concept, leveraging various geometries and configurations which embody the principles disclosed herein in order to form assemblies having non-random arrangements of materials throughout which induce Ordered Energy Localization in one or more planes of the assemblies

FIGS. 66A and 66C illustrate embodiments of a volumetric structure comprising three different substructures, while FIG. 66B illustrates an embodiment of a volumetric structure comprising two different substructures.

FIGS. 67A-C illustrate the assemblage of several different volumetric structures having differently shaped substructures.

FIGS. 68A-F illustrate further embodiments of volumetric structures having different substructure components, as well as wire models illustrating the internal structure of certain volumetric structure embodiments.

FIG. 69A illustrates an embodiment of a plurality of volumetric structures arranged in an assembly, while FIGS. 69B and 69C illustrates cross sectional views of the assembly shown in FIG. 69A along the longitudinal and transverse directions, respectively.

FIG. 70A illustrates an embodiment of a plurality of volumetric structures arranged in an assembly, while FIGS. 70B and 70C illustrates cross sectional views of the assembly shown in FIG. 70A along the longitudinal and transverse directions, respectively.

FIG. 71 illustrates an embodiment of an assembly of two different volumetric structures, wherein a first volumetric structure is configured to tessellate at the vertices of a plurality of larger second volumetric structures.

While various embodiments in accordance with the principles disclosed herein have been described above, it should be understood that they have been presented by way of example only, and are not limiting. Thus, the breadth and scope of the invention(s) should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the claims and their equivalents issuing from this disclosure. Furthermore, the above advantages and features are provided in described embodiments, but shall not limit the application of such issued claims to processes and structures accomplishing any or all of the above advantages.

It will be understood that the principal features of this disclosure can be employed in various embodiments without departing from the scope of the disclosure. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, numerous equivalents to the specific procedures described herein. Such equivalents are considered to be within the scope of this disclosure and are covered by the claims.

Additionally, the section headings herein are provided for consistency with the suggestions under 37 CFR 1.77 or otherwise to provide organizational cues. These headings shall not limit or characterize the invention(s) set out in any claims that may issue from this disclosure. Specifically, and by way of example, although the headings refer to a “Field of Invention,” such claims should not be limited by the language under this heading to describe the so-called technical field. Further, a description of technology in the “Background of the Invention” section is not to be construed as an admission that technology is prior art to any invention(s) in this disclosure. Neither is the “Summary” to be considered a characterization of the invention(s) set forth in issued claims. Furthermore, any reference in this disclosure to “invention” in the singular should not be used to argue that there is only a single point of novelty in this disclosure. Multiple inventions may be set forth according to the limitations of the multiple claims issuing from this disclosure, and such claims accordingly define the invention(s), and their equivalents, that are protected thereby. In all instances, the scope of such claims shall be considered on their own merits in light of this disclosure, but should not be constrained by the headings set forth herein.

The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and/or the specification may mean “one,” but it is also consistent with the meaning of “one or more,” “at least one,” and “one or more than one.” The use of the term “or” in the claims is used to mean “and/or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and/or.” Throughout this application, the term “about” is used to indicate that a value includes the inherent variation of error for the device, the method being employed to determine the value, or the variation that exists among the study subjects. In general, but subject to the preceding discussion, a value herein that is modified by a word of approximation such as “about” or “substantially” may vary from the stated value by at least ±1, 2, 3, 4, 5, 6, 7, 10, 12 or 15%.

As used in this specification and claim(s), the words “comprising” (and any form of containing, such as “contains” and “contain”) are inclusive or open-ended and do not exclude additional, unrecited elements or method steps.

Words of comparison, measurement, and timing such as “at the time,” “equivalent,” “during,” “complete,” and the like should be understood to mean “substantially at the time,” “substantially equivalent,” “substantially during,” “substantially complete,” etc., where “substantially” means that such comparisons, measurements, and timings are practicable to accomplish the implicitly or expressly stated desired result. Words relating to relative position of elements such as “near,” “proximate to,” and “adjacent to” shall mean sufficiently close to have a material effect upon the respective system element interactions. Other words of approximation similarly refer to a condition that when so modified is understood to not necessarily be absolute or perfect but would be considered close enough to those of ordinary skill in the art to warrant designating the condition as being present. The extent to which the description may vary will depend on how great a change can be instituted and still have one of ordinary skilled in the art recognize the modified feature as still having the required characteristics and capabilities of the unmodified feature.

The term “or combinations thereof” as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CABABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

All of the compositions and/or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the compositions and methods of this disclosure have been described in terms of preferred embodiments, it will be apparent to those of skill in the art that variations may be applied to the compositions and/or methods and in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the disclosure. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the disclosure as defined by the appended claims. 

1. An energy relay comprising: a plurality of modules assembled in a structure, each module comprising first component engineered structures and second component. engineered structures; wherein each module in the structure comprises an arrangement of the first and second component engineered structures in a substantially non-random pattern in a transverse plane of the energy relay; wherein the first and second component engineered structures are configured to cooperate to transport energy along a longitudinal plane that is normal to the transverse plane; the energy relay having substantially higher energy transport efficiency in the longitudinal plane than in the transverse plane.
 2. The energy relay of claim 1, wherein both the first and second component engineered structures are configured to transport at least 10% of the energy transported along the longitudinal plane.
 3. The energy relay of claim 1, wherein both the first and second component engineered structures are configured to transport energy through means other than internal reflection.
 4. The energy relay of claim 1, further comprising a third component engineered structure.
 5. The energy relay of claim 4, wherein the plurality of modules further comprise the third. component engineered structure, the third component engineered structure being arranged in the substantially non-random pattern in the transverse plane.
 6. The energy relay of claim 4, wherein the third component engineered structure is arranged in interstitial regions between the plurality of modules within the structure.
 7. The energy relay of claim 4, further wherein the third component engineered structure is configured to transport energy along the longitudinal plane.
 8. The energy relay of claim 4, further wherein the third component engineered structure is configured to inhibit energy transport in the transverse plane.
 9. The energy relay of claim 1, wherein the plurality of modules are periodically distributed across the transverse plane of the energy relay.
 10. The energy relay of claim 1, further wherein the substantially non-random pattern of first and second component engineered structures in the transverse plane of the energy relay comprises a transverse distortion of the substantially non-random pattern.
 11. The energy relay of claim 10, wherein the transverse distortion comprises a distortion of a boundary between adjacent first and second component engineered structures.
 12. The energy relay of claim 1, wherein the energy relay includes a first surface and a second surface, and wherein energy propagating between the first surface and the second surface travels along a path that is substantially parallel to the longitudinal plane.
 13. The energy relay of claim 12, wherein the energy is electromagnetic energy, and a variability in refractive index between the first and second. component engineered structures results in the electromagnetic energy propagating between the first and second surface to be spatially localized in the transverse plane of the energy relay.
 14. The energy relay of claim 12, wherein the energy is mechanical energy in the form of sound. waves, and a variability in acoustic impedance between the first and second component engineered structures results in the sound waves propagating between the first and second. surface to be spatially localized in the transverse plane of the energy relay.
 15. The energy relay of claim 12, wherein the energy propagating between the first surface and the second surface, upon passing through the first surface, has a first spatial resolution, and upon passing through the second surface, has a second spatial resolution that is no less than about 50% of the first spatial resolution.
 16. The energy relay of claim 12, wherein the first surface has a different surface area than the second surface, wherein the energy relay further comprises a sloped profile portion between the first surface and the second surface, and. wherein the energy propagating between the first and second surfaces is spatially magnified or spatially de-magnified.
 17. The energy relay of claim 16, wherein the sloped profile portion is angled, linear, curved, tapered, faceted, or aligned at a non-perpendicular angle relative to the longitudinal plane.
 18. The energy relay of claim 12, wherein energy with a uniform profile presented to the first surface passes through the second surface to substantially fill a cone with an opening angle of +/−10 degrees relative to the normal to the second surface, irrespective of location on the second surface.
 19. The energy relay of claim 12, wherein the energy relay includes a plurality of relay elements stacked in an end-to-end configuration in the longitudinal orientation, wherein a first element of the plurality of elements includes the first surface, and wherein a second element of the plurality of elements includes the second surface.
 20. The energy relay of claim 12, wherein the first surface is configured to receive the energy from an energy source unit, the energy source unit comprising a mechanical envelope having a width different than the width of at least one of the first surface and the second surface.
 21. The energy relay of claim 12, wherein at least one of either the first surface or the second surface is either a concave surface, a convex surface, or a fiat surface, the flat surface being sloped with a surface normal that is angled relative to the path that is substantially parallel to the longitudinal plane.
 22. The energy relay of claim 1, wherein each of the first component engineered structures and the second component engineered structure comprises at least One of: atomic or subatomic particles, glass, carbon, optical fiber, optical film, polymer or mixtures thereof.
 23. The energy relay of claim 1, wherein each of the first and second component engineered structures further comprise a cross-sectional shape of a set of one or more shapes along the transverse plane.
 24. The energy relay of claim 23, wherein the substantially non-random pattern in the transverse plane of the energy relay comprises a tiling of the cross-sectional shapes of the first and second component engineered structures, such that there are substantially no empty spaces between the first and second. component engineered structures along the transverse plane of the energy relay. 25.-64. (canceled)
 65. A method for fusing an energy relay comprising: providing a plurality of first component engineered structures and a plurality of second component engineered structures; and forming an arrangement of the first and second component engineered structures comprising a substantially non-random pattern of the first and second component engineered structures in a transverse plane of the energy relay; and wherein the arrangement of first and second component engineered structures is configured to transport energy along a longitudinal plane that is normal to the transverse plane, the arrangement having substantially higher energy transport efficiency in the longitudinal plane than in the transverse plane.
 66. The method of claim 0, further comprising processing the arrangement of first and second component engineered structures, wherein processing comprises a series of one or more steps, where each step comprises one of: applying a compressive force to the arrangement, applying heat to the arrangement, applying cooling to the arrangement, or performing a chemical reaction to the arrangement.
 67. The method of claim 66, further comprising: accommodating the arrangement of first and second component engineered structures in a constrained space prior to the processing step; and removing the arrangement of first and second component: engineered structures from the constrained space after the processing step.
 68. The method of claim 67, wherein processing further comprises applying a first compressive force to the arrangement of constrained component engineered structures along at least the transverse plane, applying heat to the compressed arrangement in one or more stages, each stage comprising a stage temperature and a stage length of time, applying a second compressive force to the heated arrangement in one or more stages, each stage comprising a stage compressive force and a stage length of time, and cooling the heated arrangement.
 69. The method of claim
 68. wherein at least one stage temperature of the one or more stages is substantially the glass transition temperature of at least one of the first or second component engineered structures, or substantially the average glass transition temperature of all of the component engineered structures.
 70. The method of claim 67, wherein processing further comprises: applying heat to the constrained arrangement; and cooling the heated. arrangement while being rested within the constrained space.
 71. The method of claim 67, further wherein applying heat to the arrangement comprises heating the constrained component engineered structures to a first temperature, and further applying heat to change the temperature of the heated arrangement to a second temperature, different than the first temperature, before applying cooling to the arrangement.
 72. The method of claim 67, wherein the constrained space is defined by a fixture comprising first and second components configured to join together to f6rm the constrained space therebetween.
 73. The method of claim 72, wherein the fixture is further configured to apply an adjustable compressive force to the constrained space.
 74. The method of claim 73, wherein the fixture is configured to release the processed arrangement after the processing step is completed,
 75. A method for forming an energy relay, the method comprising: providing a plurality of first component engineered structures and a plurality of second component engineered structures; and forming a first arrangement of the pluralities of first and second component engineered structures comprising a substantially non-random pattern of the first and second component engineered structures in a transverse plane of the energy relay; and repeating at least the following steps until the arrangement has desired engineered properties, the steps including: processing the first arrangement of first and second component engineered structures into an assembly; and heating at least a first portion of the assembly, the formed energy relay having a first transverse dimension prior to being heated; and applying a tensile force longitudinally along at least the first portion of the heated assembly, thereby altering the first portion to have a second transverse dimension, narrower than the first transverse dimension, while substantially maintaining the substantially non-random pattern of first and second component engineered structures in the transverse plane; and forming a second arrangement of a plurality of substantially similar altered first portions, where this second arrangement may be used in place of the first arrangement for further iterations of the preceding processing, heating, and applying steps.
 76. The method of claim 75, further wherein, once the first arrangement has the desired engineered properties, performing a final processing step comprising fusing the arrangement having the desired engineered properties.
 77. The method of claim 75, wherein processing comprises a series of one or more steps, where each step comprises one of:. applying a compressive force to the arrangement, applying heat to the arrangement, applying cooling to the arrangement, or performing a chemical reaction to the arrangement.
 78. The method of claim 75, wherein the heating step comprises heating the assembly of first and second component engineered structures to substantially the glass transition temperature of the first or the second component engineered structures. 79.-95. (canceled) 